(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 68661, 1424] NotebookOptionsPosition[ 52117, 1121] NotebookOutlinePosition[ 68459, 1415] CellTagsIndexPosition[ 68416, 1412] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ "Generalized second order transfer function\nPole-zero-map, Nyquist and Bode \ plots\n\n", StyleBox["H(S) ", FontSlant->"Italic"], "= ", Cell[BoxData[ FormBox[ FractionBox[ RowBox[{"1", " ", "+", " ", RowBox[{"T", " ", "S"}]}], RowBox[{" ", RowBox[{"1", " ", "+", " ", RowBox[{"2", " ", "\[Zeta]", " ", "S"}], " ", "+", " ", SuperscriptBox["S", "2"]}]}]], TraditionalForm]]] }], "Section", CellChangeTimes->{ 3.404105671464055*^9, {3.4041058687932377`*^9, 3.404105894346611*^9}, { 3.404213587340118*^9, 3.404213726194797*^9}, {3.4042141164993563`*^9, 3.4042141198459053`*^9}, 3.404263543202744*^9, {3.404428502542997*^9, 3.404428526361329*^9}, {3.404803514291835*^9, 3.4048036710571833`*^9}, { 3.4048037326798973`*^9, 3.40480375081988*^9}, {3.404803802948029*^9, 3.404803841092787*^9}, {3.404803900224763*^9, 3.404803903078836*^9}, { 3.404803944287771*^9, 3.404803994883864*^9}, {3.404804025477119*^9, 3.4048040428945847`*^9}, {3.4058481919806213`*^9, 3.405848194745288*^9}, { 3.40920423621765*^9, 3.4092042366118298`*^9}, {3.417949385595129*^9, 3.417949387262097*^9}, {3.418261874355421*^9, 3.418261884667437*^9}, { 3.440214752679172*^9, 3.4402148799776154`*^9}, 3.440216778448378*^9}, TextAlignment->Center], Cell[CellGroupData[{ Cell["Poles, zero and characteristic frequencies", "Subsubsection", CellChangeTimes->{{3.4402223608491583`*^9, 3.4402223775110493`*^9}, { 3.4402226024490147`*^9, 3.440222606022141*^9}, {3.4402226404802113`*^9, 3.44022265075847*^9}}], Cell[BoxData[Cell[GraphicsData["CompressedBitmap", "\<\ eJzNW9uOHUcVbZ/bnPFcMxNix4mjwYlBhAjEEMASiCc04YUnFMl5tEykjCAC GQsUSyDDoz/Bj/BkvsB/4C/wF/gVHvwFh1pVa1Wv6lN9Th9PIrmlc+nquuza e9fee+2q/s2d+198/uWd++d375x8cu/On744v/vnk7M/3gtF40tNc+mDpmnu nTT4vwh/+RWvm/jizWv0/9P4M16cnZ0teDWfsOzly5eL27dvx7t/ltXPz88X z549i3e/ti5evHgR7/6Rqv8w/kzio+vXr8ff0OMNtkAPDx48iHdvsezJkyeZ kP34vb14+vRpJAQfPH/06FH8j+5ASSC0uWrtHz9+7FTM4890cXp6uqBQ4idQ 1Iz4DE1AIepguPAbnkF8OyIxXs+fP49Doz1+cY8Lw4Z6zRb7Qxv0KbLxbERu oA3Gwm8g/102QRdOXttkHMkSV1LZLHNF9fE/cHSPTcAkMpNUHWbGgToxEFRA 0qCI4ouUY0jdo/tQdhT/z2Nzp1QyQzeh2Xg1gV+5VPZjLTwVJzEuOhIN+I8L rUEP6oZeRtQNkU6ZZ0GinLrC6e9kgejCc+gPLszJBBPk0XJeK3kav8euENTR scgyCSURYHpJ7KlM9LViSTqLcaB0UU3Zn/R4Rr7LmGBuGg/0g+5IXuqOt+BW HtZElqfhSqV66JLDNGN+awgv82mkBRxkkeaEWUtw+I+muA9NOMzMuZUlEWlq mSndndusZCxG1g2GAYWyMUHA762QCVRIRq07acj90CaILoP8yNiD2L2oRh+o 4wbAbZJ0irrZvLmCwW4HxxWayOA5iRYJHGpENsl8yeRoURULZpzNjDPF+b1N 3mrtm3hQdoVNMLh0dhK/Z3neWavSyBNrIgcxsZGl5gcV1kthaCvzEFCs8D+t jKmqF1w7rnBcw7rqjyukFDbq7Wx78HFjI3uKS8ZDi1MGBXVkpCQ5/HaN1DYJ dDcQZnjZKN7UDmlm7hPFAZBNZtK+rLdDU9ZGW5ltm87MZqClEGYms/QqJkhl bknHlRkU8prHYi0F8Fl2gjIb4UFQN1kmPJbVEk+lcBql6+jn5IXEbRER1EQh zrI4pnKTmngMX9xlyK6qTJQvzBq6d5f4wCBawtwWMmD75t1eBk/cLKL+UHLu J75/j4/kn726OdzmpMIVUeDRVLZqLbFwZiozO5MZ4nHjh5WJSgvFkNBHM3QM zvJDdiT1p6ijKp9wFlpCnKFGpdaQMeFOcaeHT7igmD9lIzRgX0nGI6zEtc3/ 4tTOsn+UIqPXQNm3bRA590TtTlZOmS01Uwhv4WPzM9MK+VX1gzLxe10/pPoz E4n0VgBDPMfd31L1ePMawalN/yfUM8lCwifI+JTFjliCpqm2lhk+ocrHLO7A JEI2ASM81VKWU1GcjbubLPO1KWfvC+l9lvmCS5hjWsMRQo6XjQxa8wzMNHuC MnSd3SG6gp7Qw0/ZpAaW5H/QPVkD1VawqJDVHXioMqIr0hxxN2ofzDO35dKE QnGFZ6naXl40XSQpt6fnkmkKnBJpGltxLB3OKsrzyLO+kUcYOrm6cu1sUxTL CHFaQ4iBGwinxtndo+Yx61egYPP7JPHtnipQCiEf865Z4gr0wYjAGFHrepm0 YJ6dNi4pkTgRJQjXOhf6SJQb8iDbE5uvFo/wXzyTv1YXthp6USomIdPHtlMy X83VxBEru2sS5ZeHDpukPClcQehS0dMwfLnTiy9xdfDNhYDlHxKH5bo1XGoc vqQdxiWWTXIChsmEnV7tGPtyYey1WzDUGblSNaZLqhH+N8JdroQuo0Lsrf2F pBSxOVOUHZJLZ3ON4oRWRlFsKUiqVAeErYzQMqSd9UHaqxUCh0rN9DKXKZQB 33Z7RTYXZIjkYBpS6BXM+JqlRgM6opwEoqUrXDZJgNtFS1xiigmwWSfByoiC 7wqaAgU1Ia4Bx2/3C3GtbY6hpltkuabQmVx5TYCauJI/7pvCrBIvbmRVk2S6 Ns6lJvZ7vW7Wz/nZB8otFyKmdk2yS9pNMiSTSD8sSF83rJt5IqyhNnkN1pYM LmB+axGZnK2namqRWKBedsC1wDMASxHYUZEQtwhsIfwt/4JnGknWQPUiNETm flrYcc4vL311J1SZkumokSai7kJ5Mp1bOc6jkc4LEbGJjHNnBhqtawaQz1Hk hdEZmecyT9zUorGhiL4Wn1O62k8RsAe2lbPU4kS37mslxvcr3b5XKfuW6bKm c7OfpCtkomAhmf2GKY1B5w8GEvELWwlCy1+mAeXFlIJb5MC1xL1K1pgG5KG8 7JfGP2Fdzi1O/jUClv/CzwgK9DAV/Ju0ezrm7+lRDwi9xeIO2pS4Otj0B7F4 b2mvDqKSsFGGQQyKclkkw6Uy9PRVKUJHr7cqWnDEMlfj6yxbRqrz6o4XriKC mOfFi0tSV3gVfpmY3xTbHvFZDcQqXDSuJzjKyTFH2Qj8aQJcz3GsGPqXj+Un ML8MHbeVDJJldfAZm7XboKkrnw15IUSuIod0FwOwMlcXwandFN9i0eID2SGI ZBWevZukvCme9Xi466LdAfhWSOlIP1pyLJWINv5XbEPGrq3nYNnHWIVNva8u JObaUBTYGHqG5DrwNqHbEowNANW+nbEezu7n7gbAWSdBCo0JoKn4edHt1N8l Bm6Eet+yslI3dgfrRmHSDtdVywLoUQ1FS1wcRTe0Z1wp86J71dsc2vbvyPbC 1xq+nlCsaCLRSqy1rcKh4nK4+7WLa76umnB/RVK5Cwel3g3xrIJSbaC3zLqw BAtom9iimEvGfePN3nEOKRIKSOQqLUR7Xtttp0CHQV+J/dWNdytxF5+DXjnZ V5H4cdVs1/Crd6P9a3UpbOt2u3aQpkDvuxtB4NB8qN1eA3kFdi5ge4dCXgEb l6rcgsPEFpsB8e0XgNXr4ZImeTqDMokDhRUBBnmz9Yi01JbunnXgvZaUwef4 y5NfF8S1YvlFMGwN51FcNQxbE80Vkuu8oNGrnouowWZ5GQcLp/2kbYZlr1YI xIVAXqvDeVfLrdSI/hXLHPt+nggcin3FY1PPLDrUKwPvsp5Icox8xjLHyORZ nPJrhJH/Q1Kh/Fr5fy0fKeeFu1tWpsAhJR/6ELQSsC6DH7NqBz6n4r1iCcuS 1CA0XWJMaY9pBP3IwrU6RfKLsqFQwO+yDMOgHGVHpRI5+vYEprj2hnVBqpuP WeY6fMPaitK0QOfFtirGE3ItvONWfORncWjn4p6UcjZO7jGJlqOhXdVZGHcc WnXyku3MNkb4CkskOmLCZCe3a8A/kiBr4ntEhtyz/fQDXaN2+2fSBdoiw5Ut nx7ZXdqqFk9Fsc5q8EC00jR2MrDYaulskGeR9Z2ZHpBcGNPZuMLUnI0OfvUd cGbQUwsN/NSsnOs7a0U7zWfM9MmBCC2KyPWdOcdXWGaHfFbLOjgcVF/Kr2t3 mbrD1fqqG+7ghm2p1jbc/VSUPMfEiGmanFOIVZWxopgp6jQFR/dL2+PHSz5y zTnwAt0r+NR6SX1ei/e13fxVh8etn750R1F3g/32LX5LtJXz3AyzpsXUBewE ZZVLxcUxB59bF/5yhdixtqq3Ralhqv4iBO2owiZfUR69lJqbusYibVH3ZgmR HVM609naLkbS44NqYkM6K6ej0NhfQmj3bscOcHvPsLONhINZimFd++1k9kFt 7Z4WR+NX5120IkGtwu7QRW3reGZiHZhAcUOm14X0qsw7vaIqtcn9oh0qdzYr 3DqokLBKs7xsqGZ57kbHEmRbsfz61ap2duNyTsILvUIAChlMRTbRqiKFspUR JHpFc3mnb1C76LgaHVCwFy183aw6ZfIKCZ3OBq72d8zr8rWDSVZGSlOCXNa7 Vmh+gsm2gTIYWx5m5q/IxatIF48zO/oM7siGU5nCNmuLodMMBmaqZBE7XrwG IVeprrtB1wKRW6SAxp4CIiMPsovTSz99BzHMB2Qg1a+719x1Fh571VsVrsA9 Wa+ibhDuZqfl1qapBjlgyzUOjygZYYVpOcl6FUIJj6F2U1uAro/gipIErT4O zZ7pqJ5rZOipdmxozga+xyztEwtSLJlsk5ks3zXMSanlwHurSH3ptUtctWRW G3nNisOUpk7+CpFMSTqRMi9OpFReINE7i26MKzk7gqc2Ky8C+g/urk+zfVQR lL9bpDH2rEz1VDZUpTz3M7EyHgeiq62m99SFQBzKagcGt61bkfSdSr3auQAl QRxU/rxCyyr2iN2bsMdFVb7JOMk7UlR8cmizLKMCLrcytVP9NZ78tj6Sb4Oo y30rk4b40Fq32xVyZOrEKsWL6VVsGJRyrCSCwcnMHxlpjJTybL3s00p/mqqf lN+3Mklb2uhK/iblqzgPl+9ImdL/t8K9n5SPNNrDhw+b7+ObXPgfn7vepizb N54qbS79H4z5IkE=\ \>"], "Graphics", ImageSize->{292, 114}, ImageMargins->0]], "Input", CellChangeTimes->{{3.440223824927394*^9, 3.440223825760128*^9}, 3.440223879277432*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{ RowBox[{"xmin", "=", RowBox[{"-", "2"}]}], ";", RowBox[{"xmax", "=", RowBox[{"+", "0.5"}]}], ";", RowBox[{"d", "=", "0.03"}], ";", RowBox[{"lwc1", "=", RowBox[{"If", "[", RowBox[{ RowBox[{"\[Zeta]", "<", "1"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Zeta]"}], "-", SqrtBox[ RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["\[Zeta]", "2"]}]]}], ")"}]}], ",", RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Zeta]"}], "+", SqrtBox[ RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["\[Zeta]", "2"]}]]}], ")"}]}]}], "}"}]}], "]"}]}], ";", RowBox[{"wc2", "=", RowBox[{"1", "/", "\[Tau]N"}]}], ";", RowBox[{"pole1", "=", RowBox[{ RowBox[{"-", "\[Zeta]"}], "-", SqrtBox[ RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["\[Zeta]", "2"]}]]}]}], ";", RowBox[{"pole2", "=", RowBox[{ RowBox[{"-", "\[Zeta]"}], "+", SqrtBox[ RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["\[Zeta]", "2"]}]]}]}], ";", "\[IndentingNewLine]", RowBox[{"x1", "=", RowBox[{"Re", "[", "pole1", "]"}]}], ";", RowBox[{"y1", "=", RowBox[{"Im", "[", "pole1", "]"}]}], ";", RowBox[{"x2", "=", RowBox[{"Re", "[", "pole2", "]"}]}], ";", RowBox[{"y2", "=", RowBox[{"Im", "[", "pole2", "]"}]}], ";", RowBox[{"GraphicsGrid", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ParametricPlot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", "\[Theta]", "]"}], ",", RowBox[{"Sin", "[", "\[Theta]", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Theta]", ",", RowBox[{"\[Pi]", "/", "2"}], ",", RowBox[{"3", RowBox[{"\[Pi]", "/", "2"}]}]}], "}"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"AbsoluteThickness", "[", "1.", "]"}]}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "0.5"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1.075"}], ",", "1.075"}], "}"}]}], "}"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Epilog", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"AbsoluteThickness", "[", "1.5", "]"}], ",", "Red", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"x1", "-", RowBox[{"d", " ", RowBox[{"(", RowBox[{"xmax", "-", "xmin"}], ")"}]}]}], ",", RowBox[{"y1", "-", RowBox[{"d", RowBox[{"(", RowBox[{"xmax", "-", "xmin"}], ")"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"x1", "+", RowBox[{"d", " ", RowBox[{"(", RowBox[{"xmax", "-", "xmin"}], ")"}]}]}], ",", RowBox[{"y1", "+", RowBox[{"d", RowBox[{"(", RowBox[{"xmax", "-", "xmin"}], ")"}]}]}]}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"x1", "-", RowBox[{"d", " ", RowBox[{"(", RowBox[{"xmax", "-", "xmin"}], ")"}]}]}], ",", RowBox[{"y1", "+", RowBox[{"d", RowBox[{"(", RowBox[{"xmax", "-", "xmin"}], ")"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"x1", "+", RowBox[{"d", " ", RowBox[{"(", RowBox[{"xmax", "-", "xmin"}], ")"}]}]}], ",", RowBox[{"y1", "-", RowBox[{"d", RowBox[{"(", RowBox[{"xmax", "-", "xmin"}], ")"}]}]}]}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"x2", "-", RowBox[{"d", " ", RowBox[{"(", RowBox[{"xmax", "-", "xmin"}], ")"}]}]}], ",", RowBox[{"y2", "-", RowBox[{"d", RowBox[{"(", RowBox[{"xmax", "-", "xmin"}], ")"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"x2", "+", RowBox[{"d", " ", RowBox[{"(", RowBox[{"xmax", "-", "xmin"}], ")"}]}]}], ",", RowBox[{"y2", "+", RowBox[{"d", RowBox[{"(", RowBox[{"xmax", "-", "xmin"}], ")"}]}]}]}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"x2", "-", RowBox[{"d", " ", RowBox[{"(", RowBox[{"xmax", "-", "xmin"}], ")"}]}]}], ",", RowBox[{"y2", "+", RowBox[{"d", RowBox[{"(", RowBox[{"xmax", "-", "xmin"}], ")"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"x2", "+", RowBox[{"d", " ", RowBox[{"(", RowBox[{"xmax", "-", "xmin"}], ")"}]}]}], ",", RowBox[{"y2", "-", RowBox[{"d", RowBox[{"(", RowBox[{"xmax", "-", "xmin"}], ")"}]}]}]}], "}"}]}], "}"}], "]"}], ",", "Green", ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "/", "\[Tau]N"}], ",", "0"}], "}"}], ",", RowBox[{"2.5", "d"}]}], "]"}]}], "}"}]}], ",", RowBox[{"FrameLabel", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}], ",", RowBox[{"FrameTicks", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", "None", ",", "None"}], "}"}]}], ",", RowBox[{"ImageSize", "\[Rule]", "200"}], ",", RowBox[{"BaseStyle", "\[Rule]", "monStyle"}]}], "]"}], ",", RowBox[{"Plot", "[", RowBox[{ RowBox[{"Log", "[", RowBox[{"10", ",", RowBox[{"Abs", "[", RowBox[{"Z", "[", RowBox[{"I", " ", RowBox[{"10", "^", "logw"}]}], "]"}], "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"logw", ",", "logumin", ",", "logumax"}], "}"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"AbsoluteThickness", "[", "1.5", "]"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"ImageSize", "\[Rule]", "250"}], ",", RowBox[{"Axes", "\[Rule]", "None"}], ",", RowBox[{"FrameLabel", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}], ",", RowBox[{"FrameTicks", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", RowBox[{"-", "1"}], ",", "0", ",", "1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "4"}], ",", RowBox[{"-", "3"}], ",", RowBox[{"-", "2"}], ",", RowBox[{"-", "1"}], ",", "0", ",", "1", ",", "2", ",", "3", ",", "4"}], "}"}], ",", "None", ",", "None"}], "}"}]}], ",", RowBox[{"Epilog", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"AbsolutePointSize", "[", "6", "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"logwc", ",", RowBox[{"Log", "[", RowBox[{"10", ",", RowBox[{"Abs", "[", RowBox[{"Z", "[", RowBox[{"I", " ", RowBox[{"10", "^", "logwc"}]}], "]"}], "]"}]}], "]"}]}], "}"}], "]"}], ",", RowBox[{"AbsoluteDashing", "[", RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}], "]"}], ",", RowBox[{"If", "[", RowBox[{"w1", ",", RowBox[{"{", RowBox[{"Red", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Log", "[", RowBox[{"10", ",", RowBox[{"lwc1", "[", RowBox[{"[", "1", "]"}], "]"}]}], "]"}], ",", RowBox[{"Log", "[", RowBox[{"10", ",", RowBox[{"Abs", "[", RowBox[{"Z", "[", RowBox[{"I", " ", RowBox[{"10", "^", "logumax"}]}], "]"}], "]"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Log", "[", RowBox[{"10", ",", RowBox[{"lwc1", "[", RowBox[{"[", "1", "]"}], "]"}]}], "]"}], ",", "1"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Log", "[", RowBox[{"10", ",", RowBox[{"lwc1", "[", RowBox[{"[", "2", "]"}], "]"}]}], "]"}], ",", RowBox[{"Log", "[", RowBox[{"10", ",", RowBox[{"Abs", "[", RowBox[{"Z", "[", RowBox[{"I", " ", RowBox[{"10", "^", "logumax"}]}], "]"}], "]"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Log", "[", RowBox[{"10", ",", RowBox[{"lwc1", "[", RowBox[{"[", "2", "]"}], "]"}]}], "]"}], ",", "1"}], "}"}]}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{"w2", ",", RowBox[{"{", RowBox[{"Green", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Log", "[", RowBox[{"10", ",", "wc2"}], "]"}], ",", RowBox[{"Log", "[", RowBox[{"10", ",", RowBox[{"Abs", "[", RowBox[{"Z", "[", RowBox[{"I", " ", RowBox[{"10", "^", "logumax"}]}], "]"}], "]"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Log", "[", RowBox[{"10", ",", "wc2"}], "]"}], ",", "1"}], "}"}]}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "]"}]}], "}"}]}], ",", RowBox[{"BaseStyle", "->", StyleBox["monStyle", FontWeight->"Plain"]}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"ParametricPlot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Re", "[", RowBox[{"Z", "[", RowBox[{"I", " ", RowBox[{"10", "^", "logw"}]}], "]"}], "]"}], ",", RowBox[{"-", RowBox[{"Im", "[", RowBox[{"Z", "[", RowBox[{"I", " ", RowBox[{"10", "^", "logw"}]}], "]"}], "]"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"logw", ",", "logumin", ",", "logumax"}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"FrameLabel", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\<- Im H\>\""}], "}"}]}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"AbsoluteThickness", "[", "2", "]"}]}], ",", RowBox[{"AxesOrigin", "->", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}]}], ",", RowBox[{"FrameTicks", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", "None", ",", "None"}], "}"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Epilog", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"AbsolutePointSize", "[", "6", "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{ RowBox[{"Re", "[", RowBox[{"Z", "[", RowBox[{"I", " ", RowBox[{"10", "^", "logwc"}]}], "]"}], "]"}], ",", RowBox[{"-", RowBox[{"Im", "[", RowBox[{"Z", "[", RowBox[{"I", " ", RowBox[{"10", "^", "logwc"}]}], "]"}], "]"}]}]}], "}"}], "]"}], ",", "Red", ",", RowBox[{"If", "[", RowBox[{"w1", ",", RowBox[{"Map", "[", RowBox[{"Point", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Re", "[", RowBox[{"Z", "[", RowBox[{"I", " ", RowBox[{"lwc1", "[", RowBox[{"[", "1", "]"}], "]"}]}], "]"}], "]"}], ",", RowBox[{"-", RowBox[{"Im", "[", RowBox[{"Z", "[", RowBox[{"I", " ", RowBox[{"lwc1", "[", RowBox[{"[", "1", "]"}], "]"}]}], "]"}], "]"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Re", "[", RowBox[{"Z", "[", RowBox[{"I", " ", RowBox[{"lwc1", "[", RowBox[{"[", "2", "]"}], "]"}]}], "]"}], "]"}], ",", RowBox[{"-", RowBox[{"Im", "[", RowBox[{"Z", "[", RowBox[{"I", " ", RowBox[{"lwc1", "[", RowBox[{"[", "2", "]"}], "]"}]}], "]"}], "]"}]}]}], "}"}]}], "}"}]}], "]"}], ",", RowBox[{"{", "}"}]}], "]"}], ",", "Green", ",", RowBox[{"If", "[", RowBox[{"w2", ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{ RowBox[{"Re", "[", RowBox[{"Z", "[", RowBox[{"I", "/", "\[Tau]N"}], "]"}], "]"}], ",", RowBox[{"-", RowBox[{"Im", "[", RowBox[{"Z", "[", RowBox[{"I", "/", "\[Tau]N"}], "]"}], "]"}]}]}], "}"}], "]"}], ",", RowBox[{"{", "}"}]}], "]"}]}], "}"}]}], ",", RowBox[{"ImageSize", "\[Rule]", RowBox[{"{", RowBox[{"250", ",", "200"}], "}"}]}], ",", RowBox[{"BaseStyle", "\[Rule]", "monStyle"}]}], "]"}], ",", RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"Arg", "[", RowBox[{"Z", "[", RowBox[{"I", " ", RowBox[{"10", "^", "logw"}]}], "]"}], "]"}], "/", "Degree"}], ",", RowBox[{"{", RowBox[{"logw", ",", "logumin", ",", "logumax"}], "}"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"AbsoluteThickness", "[", "1.5", "]"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"ImageSize", "\[Rule]", "260"}], ",", RowBox[{"Axes", "\[Rule]", "None"}], ",", RowBox[{"FrameTicks", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", RowBox[{"-", "1"}], ",", "0", ",", "1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "180"}], ",", RowBox[{"-", "90"}], ",", "0", ",", "90", ",", "180"}], "}"}], ",", "None", ",", "None"}], "}"}]}], ",", RowBox[{"Epilog", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"AbsolutePointSize", "[", "6", "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"logwc", ",", RowBox[{ RowBox[{"Arg", "[", RowBox[{"Z", "[", RowBox[{"I", " ", RowBox[{"10", "^", "logwc"}]}], "]"}], "]"}], "/", "Degree"}]}], "}"}], "]"}], ",", RowBox[{"AbsoluteDashing", "[", RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}], "]"}], ",", RowBox[{"If", "[", RowBox[{"w1", ",", RowBox[{"{", RowBox[{"Red", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Log", "[", RowBox[{"10", ",", RowBox[{"lwc1", "[", RowBox[{"[", "1", "]"}], "]"}]}], "]"}], ",", RowBox[{"-", "180"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Log", "[", RowBox[{"10", ",", RowBox[{"lwc1", "[", RowBox[{"[", "1", "]"}], "]"}]}], "]"}], ",", "90"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Log", "[", RowBox[{"10", ",", RowBox[{"lwc1", "[", RowBox[{"[", "2", "]"}], "]"}]}], "]"}], ",", RowBox[{"-", "180"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Log", "[", RowBox[{"10", ",", RowBox[{"lwc1", "[", RowBox[{"[", "2", "]"}], "]"}]}], "]"}], ",", "90"}], "}"}]}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "]"}], ",", RowBox[{"If", "[", RowBox[{"w2", ",", RowBox[{"{", RowBox[{"Green", ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Log", "[", RowBox[{"10", ",", "wc2"}], "]"}], ",", RowBox[{"-", "180"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Log", "[", RowBox[{"10", ",", "wc2"}], "]"}], ",", "90"}], "}"}]}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "]"}]}], "}"}]}], ",", RowBox[{"FrameLabel", "\[Rule]", RowBox[{"{", RowBox[{ "\"\\"", ",", "\"\<\!\(\*SubscriptBox[\(\[Phi]\), \(H\)]\)/\[Degree]\>\""}], "}"}]}], ",", RowBox[{"BaseStyle", "->", StyleBox["monStyle", FontWeight->"Plain"]}]}], "]"}]}], "}"}]}], "}"}], ",", RowBox[{"ImageSize", "\[Rule]", "500"}]}], "]"}]}], ",", RowBox[{"Style", "[", RowBox[{ "\"\< H(S) = \!\(\*FractionBox[\(1\\\ + T\\\ S\), \(1 + 2 \ \[Zeta]\\\ S + \\\ \*SuperscriptBox[\(S\), \(2\)]\)]\)\>\"", ",", "Bold", ",", "Medium"}], "]"}], ",", "Delimiter", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[Tau]N", ",", "10", ",", "\"\\""}], "}"}], ",", "0.1", ",", "20", ",", "0.1", ",", RowBox[{"Appearance", "\[Rule]", "\"\\""}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[Zeta]", ",", "0.9", ",", "\"\<\[Zeta]\>\""}], "}"}], ",", "0.25", ",", "3", ",", "0.05", ",", RowBox[{"Appearance", "\[Rule]", "\"\\""}]}], "}"}], ",", "Delimiter", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"logwc", ",", RowBox[{"-", "2"}], ",", "\"\\""}], "}"}], ",", RowBox[{"-", "2"}], ",", "2", ",", "0.01", ",", RowBox[{"Appearance", "\[Rule]", "\"\\""}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "w1", ",", "True", ",", "\"\<\!\(\*SubscriptBox[\(u\), \(\(c1\)\(,\)\(2\)\(\\\ \)\)]\)\>\""}], "}"}], ",", RowBox[{"{", RowBox[{"False", ",", "True"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "w2", ",", "True", ",", "\"\<\!\(\*SubscriptBox[\(u\), \(\(c3\)\(\\\ \)\)]\)\>\""}], "}"}], ",", RowBox[{"{", RowBox[{"False", ",", "True"}], "}"}]}], "}"}], ",", RowBox[{"FrameLabel", "\[Rule]", RowBox[{"{", RowBox[{"Style", "[", RowBox[{ "\"\\"", ",", "Medium"}], "]"}], "}"}]}], ",", RowBox[{"Initialization", "\[RuleDelayed]", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"Z", "[", "p_", "]"}], ":=", FractionBox[ RowBox[{"1", "+", RowBox[{"\[Tau]N", " ", "p"}]}], RowBox[{"1", "+", " ", RowBox[{"2", " ", "\[Zeta]", " ", "p"}], " ", "+", " ", RowBox[{"p", "^", "2"}]}]]}], ";", RowBox[{"logumin", "=", RowBox[{"-", "2"}]}], ";", RowBox[{"logumax", "=", "3"}], ";", RowBox[{"monStyle", "=", RowBox[{"{", RowBox[{ RowBox[{"FontFamily", "->", "\"\\""}], ",", RowBox[{"FontSize", "\[Rule]", "10"}]}], "}"}]}], ";", RowBox[{"SaveDefinitions", "\[Rule]", "True"}]}], ")"}]}]}], "]"}]], "Input", Editable->False, CellOpen->False, CellChangeTimes->{{3.419031122610962*^9, 3.419031223163603*^9}, { 3.4190312580871773`*^9, 3.419031345120612*^9}, {3.419031375667569*^9, 3.419031393758466*^9}, {3.419031424084386*^9, 3.4190315676631393`*^9}, { 3.4210538518322268`*^9, 3.421053929204443*^9}, {3.4388313391780148`*^9, 3.4388313725698423`*^9}, {3.438831417905575*^9, 3.438831433993655*^9}, { 3.438841562810161*^9, 3.438841585531909*^9}, 3.4388416179666557`*^9, { 3.438841678526017*^9, 3.4388417377604303`*^9}, {3.438841773460157*^9, 3.438841816805812*^9}, {3.438842121437399*^9, 3.438842149284706*^9}, 3.438842186058846*^9, {3.438842285658044*^9, 3.4388423190336027`*^9}, { 3.4388423601437607`*^9, 3.438842364539259*^9}, {3.43884239777216*^9, 3.4388424161481037`*^9}, {3.438842489857498*^9, 3.438842490979155*^9}, { 3.438855527831588*^9, 3.438855615295865*^9}, {3.438855646559416*^9, 3.4388557084730186`*^9}, {3.438855788523731*^9, 3.438855790683481*^9}, { 3.438856160948605*^9, 3.4388561725464697`*^9}, {3.4388562095872507`*^9, 3.438856214100995*^9}, {3.43885625464596*^9, 3.438856340611621*^9}, { 3.438856376367331*^9, 3.438856379571821*^9}, {3.4388564515361643`*^9, 3.4388566173782187`*^9}, {3.43885665164399*^9, 3.4388567299811783`*^9}, { 3.438856798284477*^9, 3.438856806096759*^9}, {3.438856861908485*^9, 3.438856862516621*^9}, {3.438856900072001*^9, 3.4388569380788803`*^9}, { 3.438856984339637*^9, 3.438857038976419*^9}, {3.438857116984556*^9, 3.43885725551167*^9}, {3.4388573205321712`*^9, 3.4388573925914583`*^9}, { 3.438857452989822*^9, 3.438857454036704*^9}, {3.438857520683799*^9, 3.438857685267655*^9}, {3.438857723687682*^9, 3.438857789179174*^9}, { 3.43886194274314*^9, 3.438862058688999*^9}, {3.4388621019116707`*^9, 3.438862166190885*^9}, {3.4388621974415617`*^9, 3.438862311382044*^9}, { 3.4388625368568983`*^9, 3.4388625569055653`*^9}, {3.438862825324873*^9, 3.438862830798663*^9}, 3.438862920795437*^9, 3.438862961001042*^9, { 3.438863017711403*^9, 3.438863040728181*^9}, {3.4388631015836487`*^9, 3.438863102300601*^9}, {3.4388632495239763`*^9, 3.438863279351087*^9}, { 3.438863369662694*^9, 3.438863375043314*^9}, {3.438863411627572*^9, 3.438863457933731*^9}, {3.43886357447574*^9, 3.43886365895088*^9}, { 3.438863693141305*^9, 3.438863706188157*^9}, {3.438863743123152*^9, 3.438863764995748*^9}, {3.438866010590251*^9, 3.438866156235344*^9}, { 3.438866291578463*^9, 3.4388662924519053`*^9}, 3.438866328471222*^9, { 3.438866540331584*^9, 3.43886655259624*^9}, {3.438927324210923*^9, 3.43892734763052*^9}, {3.4389273810691557`*^9, 3.438927443158298*^9}, { 3.4389275711125393`*^9, 3.438927625190065*^9}, {3.438927666483056*^9, 3.438927667541223*^9}, {3.4389277093670063`*^9, 3.4389277930459623`*^9}, { 3.438928813730633*^9, 3.438928814213195*^9}, {3.438928863683509*^9, 3.438928872831249*^9}, {3.438928956044507*^9, 3.438928982830037*^9}, { 3.438929032885378*^9, 3.438929037449757*^9}, 3.438929209712081*^9, { 3.438929933430447*^9, 3.4389300541192923`*^9}, {3.438930098807851*^9, 3.4389301339075327`*^9}, 3.43893018403545*^9, {3.4389302868053293`*^9, 3.438930288055539*^9}, {3.4390020288647547`*^9, 3.4390021496657124`*^9}, { 3.439002191713994*^9, 3.4390022874382677`*^9}, {3.439002361969541*^9, 3.439002440313871*^9}, {3.439002495684845*^9, 3.439002496423717*^9}, { 3.4390025706480207`*^9, 3.439002581254114*^9}, {3.43900261283292*^9, 3.439002614327114*^9}, {3.43900271467373*^9, 3.4390027195402107`*^9}, { 3.4390027680282707`*^9, 3.4390027696184072`*^9}, {3.439002851659795*^9, 3.439002855149198*^9}, {3.439002917219688*^9, 3.4390029232809753`*^9}, { 3.439003352716712*^9, 3.439003392146304*^9}, 3.439004478687106*^9, { 3.4390045131291237`*^9, 3.4390045144703207`*^9}, {3.439004581683967*^9, 3.4390046110822678`*^9}, {3.4390046436751003`*^9, 3.439004646809518*^9}, { 3.439080641218726*^9, 3.4390806416843*^9}, {3.439080686397265*^9, 3.439080714635808*^9}, {3.439080759101329*^9, 3.439080766231585*^9}, { 3.439080820424378*^9, 3.43908088716971*^9}, {3.4390809206270523`*^9, 3.439080927963367*^9}, {3.439081065690084*^9, 3.439081112054818*^9}, { 3.439081188712358*^9, 3.439081213359221*^9}, {3.4390813264631653`*^9, 3.439081419580738*^9}, {3.439081457407688*^9, 3.43908158968629*^9}, { 3.439081837827588*^9, 3.4390819693966217`*^9}, {3.43908212092999*^9, 3.4390821803904257`*^9}, {3.4390823475859537`*^9, 3.4390823649530573`*^9}, {3.439082408419166*^9, 3.439082409576627*^9}, { 3.4390824592664137`*^9, 3.4390824622078753`*^9}, {3.4390825116150217`*^9, 3.439082517185548*^9}, {3.4390825755617313`*^9, 3.439082576695953*^9}, { 3.44021400343113*^9, 3.440214004913499*^9}, {3.440214565056889*^9, 3.440214570855123*^9}, {3.440214920226482*^9, 3.440214931067995*^9}, { 3.440214964679274*^9, 3.440214966079544*^9}, {3.4402162354719048`*^9, 3.4402163077023773`*^9}, 3.440216463643137*^9, {3.440222846308989*^9, 3.440222872760551*^9}, {3.440222905651259*^9, 3.440222908243331*^9}, { 3.440223009926021*^9, 3.44022303340406*^9}, {3.440223093610271*^9, 3.4402230942004213`*^9}, 3.4402231563605347`*^9, 3.440223210756966*^9, { 3.44024822661604*^9, 3.440248241084302*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`logwc$$ = -2, $CellContext`w1$$ = True, $CellContext`w2$$ = True, $CellContext`\[Zeta]$$ = 0.9, $CellContext`\[Tau]N$$ = 10, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[ Style[ " H(S) = \!\(\*FractionBox[\(1\\ + T\\ S\), \(1 + 2 \[Zeta]\\ S \ + \\ \*SuperscriptBox[\(S\), \(2\)]\)]\)", Bold, Medium]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`\[Tau]N$$], 10, "T"}, 0.1, 20, 0.1}, {{ Hold[$CellContext`\[Zeta]$$], 0.9, "\[Zeta]"}, 0.25, 3, 0.05}, {{ Hold[$CellContext`logwc$$], -2, "log u"}, -2, 2, 0.01}, {{ Hold[$CellContext`w1$$], True, "\!\(\*SubscriptBox[\(u\), \(\(c1\)\(,\)\(2\)\(\\ \)\)]\)"}, { False, True}}, {{ Hold[$CellContext`w2$$], True, "\!\(\*SubscriptBox[\(u\), \(\(c3\)\(\\ \)\)]\)"}, {False, True}}}, Typeset`size$$ = {500., {185., 190.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`\[Tau]N$11252$$ = 0, $CellContext`\[Zeta]$11253$$ = 0, $CellContext`logwc$11254$$ = 0, $CellContext`w1$11255$$ = False, $CellContext`w2$11256$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`logwc$$ = -2, $CellContext`w1$$ = True, $CellContext`w2$$ = True, $CellContext`\[Zeta]$$ = 0.9, $CellContext`\[Tau]N$$ = 10}, "ControllerVariables" :> { Hold[$CellContext`\[Tau]N$$, $CellContext`\[Tau]N$11252$$, 0], Hold[$CellContext`\[Zeta]$$, $CellContext`\[Zeta]$11253$$, 0], Hold[$CellContext`logwc$$, $CellContext`logwc$11254$$, 0], Hold[$CellContext`w1$$, $CellContext`w1$11255$$, False], Hold[$CellContext`w2$$, $CellContext`w2$11256$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`xmin = -2; $CellContext`xmax = Plus[0.5]; $CellContext`d = 0.03; $CellContext`lwc1 = If[$CellContext`\[Zeta]$$ < 1, {1, 1}, {-(-$CellContext`\[Zeta]$$ - (-1 + $CellContext`\[Zeta]$$^2)^ Rational[ 1, 2]), -(-$CellContext`\[Zeta]$$ + (-1 + \ $CellContext`\[Zeta]$$^2)^Rational[1, 2])}]; $CellContext`wc2 = 1/$CellContext`\[Tau]N$$; $CellContext`pole1 = \ -$CellContext`\[Zeta]$$ - (-1 + $CellContext`\[Zeta]$$^2)^ Rational[ 1, 2]; $CellContext`pole2 = -$CellContext`\[Zeta]$$ + (-1 + \ $CellContext`\[Zeta]$$^2)^Rational[1, 2]; $CellContext`x1 = Re[$CellContext`pole1]; $CellContext`y1 = Im[$CellContext`pole1]; $CellContext`x2 = Re[$CellContext`pole2]; $CellContext`y2 = Im[$CellContext`pole2]; GraphicsGrid[{{ ParametricPlot[{ Cos[$CellContext`\[Theta]], Sin[$CellContext`\[Theta]]}, {$CellContext`\[Theta], Pi/2, 3 (Pi/2)}, PlotStyle -> AbsoluteThickness[1.], PlotRange -> {{-2, 0.5}, {-1.075, 1.075}}, Frame -> True, Epilog -> { AbsoluteThickness[1.5], Red, Line[{{$CellContext`x1 - $CellContext`d ($CellContext`xmax - \ $CellContext`xmin), $CellContext`y1 - $CellContext`d ($CellContext`xmax - \ $CellContext`xmin)}, {$CellContext`x1 + $CellContext`d ($CellContext`xmax - \ $CellContext`xmin), $CellContext`y1 + $CellContext`d ($CellContext`xmax - \ $CellContext`xmin)}}], Line[{{$CellContext`x1 - $CellContext`d ($CellContext`xmax - \ $CellContext`xmin), $CellContext`y1 + $CellContext`d ($CellContext`xmax - \ $CellContext`xmin)}, {$CellContext`x1 + $CellContext`d ($CellContext`xmax - \ $CellContext`xmin), $CellContext`y1 - $CellContext`d ($CellContext`xmax - \ $CellContext`xmin)}}], Line[{{$CellContext`x2 - $CellContext`d ($CellContext`xmax - \ $CellContext`xmin), $CellContext`y2 - $CellContext`d ($CellContext`xmax - \ $CellContext`xmin)}, {$CellContext`x2 + $CellContext`d ($CellContext`xmax - \ $CellContext`xmin), $CellContext`y2 + $CellContext`d ($CellContext`xmax - \ $CellContext`xmin)}}], Line[{{$CellContext`x2 - $CellContext`d ($CellContext`xmax - \ $CellContext`xmin), $CellContext`y2 + $CellContext`d ($CellContext`xmax - \ $CellContext`xmin)}, {$CellContext`x2 + $CellContext`d ($CellContext`xmax - \ $CellContext`xmin), $CellContext`y2 - $CellContext`d ($CellContext`xmax - \ $CellContext`xmin)}}], Green, Circle[{(-1)/$CellContext`\[Tau]N$$, 0}, 2.5 $CellContext`d]}, FrameLabel -> {"Re S", "Im S"}, FrameTicks -> {{0, -1}, {0, -1, 1}, None, None}, ImageSize -> 200, BaseStyle -> $CellContext`monStyle], Plot[ Log[10, Abs[ $CellContext`Z[ I 10^$CellContext`logw]]], {$CellContext`logw, \ $CellContext`logumin, $CellContext`logumax}, PlotStyle -> AbsoluteThickness[1.5], Frame -> True, ImageSize -> 250, Axes -> None, FrameLabel -> {"log u", "log |H|"}, FrameTicks -> {{-2, -1, 0, 1, 2}, {-4, -3, -2, -1, 0, 1, 2, 3, 4}, None, None}, Epilog -> { AbsolutePointSize[6], Point[{$CellContext`logwc$$, Log[10, Abs[ $CellContext`Z[I 10^$CellContext`logwc$$]]]}], AbsoluteDashing[{2, 2}], If[$CellContext`w1$$, {Red, Line[{{ Log[10, Part[$CellContext`lwc1, 1]], Log[10, Abs[ $CellContext`Z[I 10^$CellContext`logumax]]]}, { Log[10, Part[$CellContext`lwc1, 1]], 1}}], Line[{{ Log[10, Part[$CellContext`lwc1, 2]], Log[10, Abs[ $CellContext`Z[I 10^$CellContext`logumax]]]}, { Log[10, Part[$CellContext`lwc1, 2]], 1}}]}, {}], If[$CellContext`w2$$, {Green, Line[{{ Log[10, $CellContext`wc2], Log[10, Abs[ $CellContext`Z[I 10^$CellContext`logumax]]]}, { Log[10, $CellContext`wc2], 1}}]}, {}]}, BaseStyle -> $CellContext`monStyle]}, { ParametricPlot[{ Re[ $CellContext`Z[I 10^$CellContext`logw]], -Im[ $CellContext`Z[ I 10^$CellContext`logw]]}, {$CellContext`logw, \ $CellContext`logumin, $CellContext`logumax}, PlotRange -> All, FrameLabel -> {"Re H", "- Im H"}, PlotStyle -> AbsoluteThickness[2], AxesOrigin -> {0, 0}, FrameTicks -> {{0, 1}, {0, 1}, None, None}, Frame -> True, Epilog -> { AbsolutePointSize[6], Point[{ Re[ $CellContext`Z[I 10^$CellContext`logwc$$]], -Im[ $CellContext`Z[I 10^$CellContext`logwc$$]]}], Red, If[$CellContext`w1$$, Map[Point, {{ Re[ $CellContext`Z[I Part[$CellContext`lwc1, 1]]], -Im[ $CellContext`Z[I Part[$CellContext`lwc1, 1]]]}, { Re[ $CellContext`Z[I Part[$CellContext`lwc1, 2]]], -Im[ $CellContext`Z[I Part[$CellContext`lwc1, 2]]]}}], {}], Green, If[$CellContext`w2$$, Point[{ Re[ $CellContext`Z[I/$CellContext`\[Tau]N$$]], -Im[ $CellContext`Z[I/$CellContext`\[Tau]N$$]]}], {}]}, ImageSize -> {250, 200}, BaseStyle -> $CellContext`monStyle], Plot[Arg[ $CellContext`Z[I 10^$CellContext`logw]]/ Degree, {$CellContext`logw, $CellContext`logumin, \ $CellContext`logumax}, PlotStyle -> AbsoluteThickness[1.5], Frame -> True, ImageSize -> 260, Axes -> None, FrameTicks -> {{-2, -1, 0, 1, 2}, {-180, -90, 0, 90, 180}, None, None}, Epilog -> { AbsolutePointSize[6], Point[{$CellContext`logwc$$, Arg[ $CellContext`Z[I 10^$CellContext`logwc$$]]/Degree}], AbsoluteDashing[{2, 2}], If[$CellContext`w1$$, {Red, Line[{{ Log[10, Part[$CellContext`lwc1, 1]], -180}, { Log[10, Part[$CellContext`lwc1, 1]], 90}}], Line[{{ Log[10, Part[$CellContext`lwc1, 2]], -180}, { Log[10, Part[$CellContext`lwc1, 2]], 90}}]}, {}], If[$CellContext`w2$$, {Green, Line[{{ Log[10, $CellContext`wc2], -180}, { Log[10, $CellContext`wc2], 90}}]}, {}]}, FrameLabel -> { "log u", "\!\(\*SubscriptBox[\(\[Phi]\), \(H\)]\)/\[Degree]"}, BaseStyle -> $CellContext`monStyle]}}, ImageSize -> 500]), "Specifications" :> { Style[ " H(S) = \!\(\*FractionBox[\(1\\ + T\\ S\), \(1 + 2 \[Zeta]\\ \ S + \\ \*SuperscriptBox[\(S\), \(2\)]\)]\)", Bold, Medium], Delimiter, {{$CellContext`\[Tau]N$$, 10, "T"}, 0.1, 20, 0.1, Appearance -> "Labeled"}, {{$CellContext`\[Zeta]$$, 0.9, "\[Zeta]"}, 0.25, 3, 0.05, Appearance -> "Labeled"}, Delimiter, {{$CellContext`logwc$$, -2, "log u"}, -2, 2, 0.01, Appearance -> "Labeled"}, {{$CellContext`w1$$, True, "\!\(\*SubscriptBox[\(u\), \(\(c1\)\(,\)\(2\)\(\\ \)\)]\)"}, { False, True}}, {{$CellContext`w2$$, True, "\!\(\*SubscriptBox[\(u\), \(\(c3\)\(\\ \)\)]\)"}, {False, True}}}, "Options" :> {FrameLabel -> { Style[ "ER@SE/LEPMI, 2009. Hosted by Bio-Logic@www.bio-logic.info", Medium]}}, "DefaultOptions" :> {}], ImageSizeCache->{542., {317.875, 323.125}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>(($CellContext`Z[ Pattern[$CellContext`p$, Blank[]]] := (1 + $CellContext`\[Tau]N$$ $CellContext`p$)/( 1 + (2 $CellContext`\[Zeta]$$) $CellContext`p$ + $CellContext`p$^2); \ $CellContext`logumin = -2; $CellContext`logumax = 3; $CellContext`monStyle = {FontFamily -> "Helvetica", FontSize -> 10}; SaveDefinitions -> True); Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{{3.4388556027690277`*^9, 3.4388556160850563`*^9}, { 3.43885565321496*^9, 3.4388557093123713`*^9}, 3.4388557917618933`*^9, { 3.438856164193565*^9, 3.438856173787301*^9}, {3.438856289480974*^9, 3.4388563074872*^9}, 3.438856341922669*^9, 3.438856383834568*^9, { 3.438856454866268*^9, 3.438856618033578*^9}, {3.438856671361848*^9, 3.43885673077092*^9}, 3.43885680781791*^9, {3.4388569166867237`*^9, 3.438856939226519*^9}, {3.438857002274947*^9, 3.438857039625173*^9}, 3.438857090476747*^9, 3.4388571312052517`*^9, {3.4388571616105213`*^9, 3.438857255873385*^9}, {3.438857358068408*^9, 3.438857393215371*^9}, 3.438857454767692*^9, {3.4388575211050797`*^9, 3.438857550745728*^9}, { 3.438857590606422*^9, 3.4388576856459427`*^9}, {3.438857726928344*^9, 3.4388577896003304`*^9}, 3.438861948203452*^9, {3.4388619973936787`*^9, 3.438862060330573*^9}, {3.438862105330358*^9, 3.438862135413135*^9}, { 3.4388622272495937`*^9, 3.438862243855588*^9}, {3.4388622786279984`*^9, 3.438862311821351*^9}, {3.43886253805145*^9, 3.438862557344297*^9}, 3.438862832049555*^9, 3.438862924082696*^9, 3.43886296297782*^9, 3.43886304275257*^9, 3.438863103207814*^9, {3.438863269876977*^9, 3.438863280619543*^9}, {3.4388633879852858`*^9, 3.4388634138338737`*^9}, 3.438863459153843*^9, 3.438863661127224*^9, 3.4388637065293818`*^9, 3.4388637653364573`*^9, {3.438866066252674*^9, 3.438866095717321*^9}, 3.438866158875689*^9, 3.4388662932464123`*^9, 3.4388663289354763`*^9, { 3.4388665412524023`*^9, 3.4388665529484377`*^9}, 3.4389272724388742`*^9, 3.438927349657247*^9, {3.438927418380189*^9, 3.438927446566152*^9}, { 3.4389275734883957`*^9, 3.438927591679677*^9}, 3.438927626178763*^9, 3.438927668271693*^9, 3.438927795422224*^9, 3.4389288144593782`*^9, 3.438928873700079*^9, {3.438928956452901*^9, 3.4389289831533737`*^9}, 3.4389290384871387`*^9, 3.438929210085512*^9, 3.438929951666382*^9, 3.4389301352543287`*^9, 3.4389301860186033`*^9, 3.438930288996696*^9, 3.439001959017565*^9, 3.439002288417509*^9, 3.439002441382902*^9, 3.4390025110151052`*^9, 3.439002582300859*^9, 3.439002615291629*^9, 3.439002720764079*^9, 3.439002770625774*^9, 3.439002856096375*^9, 3.439003393483251*^9, 3.4390044805317087`*^9, 3.439004531038945*^9, { 3.439004590959837*^9, 3.4390046120358553`*^9}, 3.4390046487295713`*^9, 3.439080517191153*^9, 3.439080644233012*^9, 3.4390807161942177`*^9, 3.4390807688192587`*^9, 3.4390808439506187`*^9, 3.4390808885582533`*^9, 3.439080928278043*^9, 3.439081115675048*^9, 3.439081214211994*^9, { 3.439081333248664*^9, 3.4390813733045464`*^9}, 3.4390814223415527`*^9, 3.4390814995631742`*^9, 3.439081544184862*^9, 3.4390815936343*^9, { 3.43908184721448*^9, 3.439081904019261*^9}, 3.4390819341803293`*^9, 3.439081972808069*^9, {3.4390821325169373`*^9, 3.43908218165336*^9}, { 3.439082352897978*^9, 3.4390823658623962`*^9}, 3.439082410466275*^9, 3.4390824635525637`*^9, 3.4390825211541157`*^9, 3.4390825780085917`*^9, 3.440214005841449*^9, 3.440214571356855*^9, 3.440214934719429*^9, 3.4402149667034283`*^9, 3.440216237713449*^9, {3.4402162822119017`*^9, 3.440216308180284*^9}, 3.440222827750651*^9, 3.440222873089723*^9, 3.440222909008399*^9, 3.440223034256981*^9, 3.440223095182577*^9, 3.440223156954173*^9, 3.440223211827736*^9, {3.4402482575528193`*^9, 3.440248271035818*^9}}] }, Open ]] }, Open ]] }, Open ]] }, WindowSize->{886, 772}, WindowMargins->{{192, Automatic}, {Automatic, 84}}, DockedCells->FEPrivate`If[ FEPrivate`SameQ[FEPrivate`$ProductIDName, "MathematicaPlayer"], FEPrivate`Join[{ Cell[ BoxData[ GraphicsBox[ RasterBox[CompressedData[" 1:eJztXXlYU9e27/fe++Pe9757be9tax1AkUGQAMokiLMWB9Q60Dreaq2tA1Zb LaJ1wjrVjg44KyKCAzIj8zwFSBjCkDCEBAjIKELRKhqSvJ3ssNmckxNGxX7d v+/od7LPPmuvtWJ+a++19jnqbdy5fON/v/XWWybgz//811tvKc9FA4RQmDVv AVdnbMpy5+KEBNgm7kT6t3uleuMbxxrVsqbI7T6WTVsrn7paNvPTRs87VUUC cNREx7e67HlpOVNhYt0x3qJ11LiaS1cGqhIBAQEBwWtHzg0vro5eps5Yjv74 /E9WC27fEeXmivLzM8+eZxtYKsYayMaMe2Y+U+a0S7b8oMz5kHzpfrnjVy+W 7nzh9EWHzbIO8w87TB1emDk817doHG1QFRM71AYREBAQEPQBcPIvSE8vMDQW 6Ojl6+oV6Izj6RrwLOx5do6RJrP4rKkKvTGKMWM7DFjta09Jt17r2HpV+qWH 7LOzslUnpEu+kzp+JbVb9XLS/OesqfW6E+qMLcuzOENtFgEBAQFBHwBjQXlp abb91OLRY4vG6BeNHc83sMgzss+fuCTefnXTBGtlLNA36NAf92TGCrHbrao9 ng/3eDV/6/lsx+WOLz2kq49L5++UOqxsmzBDomsumTRFxOMNtVkEBAQEBL0F KgqA87yNm0Sjxlbqm/KMJ2bOcWQvWpa6Ym2881q+48ziD2cK5s8VLFrIn+WQ vv6LxO2uydt2sbd/m73dNX/rbv7nXwvWbSlyXpuz4COuiW2x9YzygoKhtoyA gICAoFcQY1B+PORerWPEs5hceuFoTcDl6oBrVUFekkDPOr+Ldfcv1gVcrgu8 Wud/ufb+JUnYrapwH8kDn+oHPjXhPg/DbtWGeD8MvFETdE3sezZ2ynRBarr2 octLSrL9A4TpPXQjICAgIHilAPxf0Ql1MPjukGScde5XX9QG3mgIDquLSJTE pLeFR/4REvokLKItMrYtJq4tNq4tLKwlKrohh9eQV9CYndfIyW1iZz9OZIP+ 1YHhkrDwIo+LkSs3Zoc+KBcK8RFLBQJuYmLU6dMRn2/irFojuXCpoqhoiKwn +OtCGBIi9PYeai0ICIYYaCEAo0ClCspwIBKVLFsrMZ+Xf9i1NiywKTGnNjWv IT6Nf/Fic0zis6z8p5m8p5m5Tzh5T9I5TxKS29LYLUWlzcWipkJhU1ZBXSK3 Ijq9PCKlIiGjPDQueJzdzeFjr1ja+i1c4rXc+ecFC/c4TNltPP63d98LGz6i Zt16SWrqUHuC4K8IEAj4b70FDoGODjh/RaOkD9GCNzw83MXF5eTJk3w+f0gU IPgTAY8FIApUqSAuLc0/fKzUdK5w5voc971VUQ+q0/IakjJaElNCJk9JsZ/O v+7VnFPQmlvYkp3fks1rYXPApZa4+OaU1EcpqfVxiVVRCeWhMSWh0WUxifyQ 8O8/GLln2Du/Dnv/0N//8fXf/vf0P4dFvvd+wwjdjgkT6695DrUPCP7SKN28 uWTVKmU4GDasPClp0OXn5ORcuHBh0MX2BiAGBQQE7Nu3z9OT/MoIqBCks1Nu 3ky+dSs3MbEkPx/M/8uFwjI+v4TDKYqN5QcE8c56ZC1emWU4NdPOOWOhC9fd reJBYH1M0u+xSY/SOckLFj3UMc4bZZC0co0gKLQuO7+Ry6tncxpSMhrjkxoj ImtDgiVBASJ/v5K7t/N9bhUEB2beu/PV8A/OjxzvM1zHb/jIsrF6ckMjhZ5e h4VVddiDofYHAYESICKAcFDs4DDokocwFkD4+vqCcDCEChC8mRALBNX3Ajkr Pz2vb3hk5Ae/WVl62NoGWtukWdlmTrLhWNvzJ08rsbARmjlUWs5usJ7J27e9 +r53U0RMU2Law/Ss2PlO5QbmFaY2pXqmKfoTEnd8LQiPrmJzq5LYkrgkSWS0 JChY7O9fcvdOka9Pzs0bOf5+/Lv3ci1mSEwdpJNmyFl2cpOJCv3xHRYTq6Oj X6mlQm/vwcoDl+fmKqW9shwCwZADrAhgsmjQawdDHgvA6sDFxWWo8lQEbz4k Sanir77JMbVINxgfbTSeYz6xzX66YrKDwmKSwshQoT9GYTBOMX5CjpuL+N6t h5HxkvhUUUp6xDynIiOLIpYNn2VbYmqTO9YkYpJt8vEfBFHx5XEpwvCoMv+g 0jv3Cn198ry9Mjyv8e/fb4xKlq8/IluyQzZtldxmvtzERmZq9TA4uPeqAiqG v1NwgHPUDhb1Gn+/cI6HDvARXQITP3z6R/kIoL5lzx7UUnb8OBoI9ASX0C3w nN/50g+gBkUfujRcrFIOi4UPrUxTdBoIExdIeWQUaAfEBRQABwpP4ESgo4Py 3vBeJBwRXdm5c8iloA+0C9xSsnAh1BlqhfxMvxGOArUCfaADgRxgI5AAtaK7 DmpC0QqqDYZW+5bFgo7qugsY6O0NxgInoJHuQ1wZCiia4/4BosCh/Cq734i+ 4m5yGBxF9wwTtMcCwNLh4eGURpjnpwg5efKkiwru7u7x8fGo/bffftu1axdo x3NBuFjQB3wEqwMtOkAAOUAaRR+kDBgUDA17AmVQcAEdoAIBAQF0i9BHmK1C QnArcOGwD/gbSqPI5/P5wJlIVdATnMNqCBwINMKreFqM4g2NntT+pYAhoA6o BZiP5ODeoDtE44javaFFOFzlQUfh3ynFRqAAuJFumhaIU9PEn216PMmm1ca+ berMduspcj0DxVgdhZGR3GySgmWb5ba95M4tcUScMCaxJCHZ33F+qqF5Bsua rToyzGwyTCzDdQzuz56bcsajKCS8ODCI7+PD8/LiXL/Gvnq5LDpRkpT5cs8F 2WcnZU7bZVOWKVjTms5c7JOSiGNxmsUDBE62iDPBCX4Or/YjFiA2A41dxDXg WICqloj8KZ3VQUfFnIiiwUcwND0IIsUgLaP+XVZA2uwUDg2HhkCBQIJI0/SY cqOaz1Xmw3O1EBYLaUVxHdRKyerd3QXG6gqyKrvAgRQA40LFYB+NPoRWMyV2 cM3VgWDYMKVMHR0Ua+hfB2VqweQoumeY0GMsQKSHAFpw2oE/bUAXASoAuoMk AAkKcgJoB3+DPnSxUJoWZgBXgYZIOPgI/kblZqQMoBrUDQwEhoZ9gAJAOGiE lEWxCH2EcsBdUFs4ELwFGgKFgKs4kVLkAwWQBNCI8zMKEEgIHhkRLWv0ZI9f CugGmRn/RqBWSBPQSFeYaUQt3tAiHKoB7ALt4G88xCOdgTPBcECHfmwYEIvF VWc8nk+bLbObLrWdJTWbIRunr9DTlZvbyCd/yHZ1KfLxKg2L4ofHFEbFes2Z e0fP2N/Y4j52BJhY3NMzvjJqzO3lzhmXrxT4+OZd90y5dDHH905hbHJpXGrL gcuy7WdlKw/Kp69tX7ZJ1H1zaY9AHIL/9PAAgX6eKEBQGBVRbl9jARoFMTZg rUGJBegq7Ny1oaWzgomkoYEA+agH6uxM4XYYOJQZrc4OlGAB1aZfhcPBEwr3 UvgWNxkOCiIC5RLV/M5FBGVc1B+NBXNxaoernABaIOVqJHyK/ynANVfP4TsX Fyh04uZD5+NjaXeU9kiEMPBYAG7X+NMGbMD0k8fFAjKBM0kmcqDoACaokFQ1 KgMBRKGJKBP5Uz5COfglQFnQM3DpgbgUfkQ98XNInkgCnDyjbni8g+GAIoHJ k9odAkMVnMDDFigHvwV8RN8yfjvTiFq8oUU4xXyNNsJ1InJmX1FZWVkTFS39 cJHCbGqHnbN03jappb1cV0duYZfqui3P+3pR4ANecHheWMT5mbN+Ga13Tt/4 bPcDtHjoG/8yQveUrt7djRsTzpzJuno1OzQqLzK+KDrxofuVl67nZRuOy2du qL/Xh+wQhPpHpyJhCvOocxSdJAkW7DiTiGhr+T7HAtrsfbByRGh0eBXnImQj kkZXA87JURBUB4thw5gMwTvgUYZJKybJXTaGhOArFwiNqw8kiqIVE5NDJ6Dc C1zj4KYh0B2OA9cc/hNCy8Ou5U9nkk2dslNN/rsCtFZH0X2uEQOPBUwbgQB7 MG0QwmeJkLQ1JqOYdIAKoGwGPRbA5Azs0KdYgLMijGUah9ASC3Dh+I2UcWFm jLJU6eWWKoooSLn4WHQ5yBbK7UwjavEGk3BY98FJnm4j6AlUHUhtqKKioqqq qjY5tWP6Yrntx7IV3z3acrpt2gLFOEO267aiOzdLH0QXRUQXRsZemj3nrK7B RcMJGo9LRqYX9E1+fW/UVXOLhGNH86LiBIlpJXGpVe6Xn7iel288Lpu/tTqp z3pChqEk2NXpdDTtV5G/RnrB+acfOSJ1DFq4EPLGIMYCmMKCVAnvRVwEzYFD w9tRsl2d2FdFPURE9CBI4WGcw9E5kEw5RPQ1SPeJOm6Usl7QGaDVzsEsQh+R KFH3pQRTLEDkD4wCQ6C1nsbavRYPdzM5JAStd+i+RcoAzaEn1QsorY7C5Wv8 fiEGHgvwHA4EmpBT2gEgVyCxMAoAzgFzZjTV740OgFKg2hRlAM+gPJLG27XE AjSJpZjZ+1gAc0TAKMiilFhASf7TVy5MntTiELgogJkcprhD1wRXXuOIWrzB JFxjUMZNg6skpojfS8BYAFYH9UGhcqslsmX7WlzOFu4+1zxlTrabi9DftyIm sSw2qSQ+6bbj/FBDswiWlYbD1CrceGKUuWXmcqe0vS7xly6UxCWJ2dyKtCyJ +6XHbuc6tvykmLez4YZfn3RDVIBOYDv8LSvrlaoTOI18FbEAVg/5WDF6sGKB ms9VVAkJUEmqKiGQLdWTf2wpBMMifqBcCr97KZPOw3wsT0IR0iUNz9LA8jFN Mr5Aw0ur6NCwTEOrKkwrevzCPQNHwQ+N5WOUsoMUDcMH+uLwG/E6NTq6fKtS DC8uwC9Ri6Mo8pkwKLGADqZ2xAwoYwAzJ3Ty0a4DuAtWH3BlYN0WZr+Zbn+l sUCkmiTDMgHuChFDLKB4g8mTWhyC8jD9jgUaR3wVsQDGHbo5vYdYLK7sBDh/ tn6XfOHOZy6nha4X8r/5Ofu7r8QBvtVxyeLEtLLk9MD5C9INzTlmNlks1dF5 kmlixZlgWeg4u8BtS8KFX3kRUVXZ+ZVpmVVsjoTNrfn+8iPXM9LNp+RLvpU6 bqrK6kMuS508UbEHvn5HJIwWCKLByxEhiuimiWpGjRdPBxgLkG7gBIrCAxZo VM+QMT4XoQ2u3t7q5RJlh0/nWBpWCnAmrMqTUDYpdc29vb2ZyJ+yowlPDUFb wL0U8qdXovF9SspaAHNdGLlU6fPuGR4c9DCtXFB0kjNFc7VM1fdISXDh+TqU L9LuKFH34hETeowF+LwRru7pOSI8Sxyg2oJCbxdhfIgoAmWYYT6BadsMPRZA 2seVgXkhes/exwIKlfUjR4QAHAX0gfVTjd1we9ElJk8yWYQWBRQl+5Qj0jii Fm/0O0cE12sDWRegh45hLGg9cEo+98uXX/xUu9uDd+Ay96hbdeDtuoTU6pQM UWpG5DynYgOLElObElNr1d82JSZWJcaTKqY6iF3WZXicSvb1zfa7X8fNrc/m 1Wdw67Jy6tjZdQc9Wveel244IlvqqrBb2b5sS2VOXi/V65aT6Zy8qTMqqh8y 3mGwasdw3wtsAYSGT1whL1GyHJB8ENGp58woDDHPG1FuHI8FaGlAKRMoNcG3 1FJ2+HQvZaLRUcYGJy54FW1hpVCculzLYqmdprpR6RMsEdQVAbEMiYZtSN3Z XmP5GEnGgbfg8ZcC/CtAkRoFMsqNuEzKVis8FiC1lZFRq6PQcFrCWY+xAAee lkG8DRrRBiERNtWnFBlROkjUSUeQvVH2mCl33ctYQN/pqvF2Fyx9JKLFApyp gFGwZ59iAZ5jpxRPKbVjijdEzJ5ksgiXT1kf9b52rHFELd4YSO1Ye2FIO/AX UCjfRFQmbP9og2z2RtmG4627z5fsu5B98kBt6L3mhJSGtKxqdlbcfKcKffOK CdbKw8Sqwmhi9SSb2nVL8391z/T3KwoNLwh9UBQU3MDJfZSd35yR08LNa8nI btlxom3Hz9L17rIF2+TT1ynMHF8sWCNJSu6NhvQJG/gBohMRVnWF/Xu5pxTu MFfvG1dtNcSTJygVA+elkFHxPaWwMyIi9WbFTmnKjywWEqLlzQbIOjwWiLCl Ac48cBMmRROU5Ee7H1FCu0sfHR2UckGhAdVfkDTkQ/QRv1FtV+coXaWK48eV G+9XrVLq0NkZsC5c7KBd/XCnq4hhn5LSLihBta1UpIpH6swPerACq0EjoLUY WsWoBaoWU5SFGxhCaS/4hwEU63QOvKRxCgGDiBZHodoKfZMqQv9yRLtUADcC Psc3GUKKhmEC368IaYGSw6ewCj537VEHuPtIhHEgvvMTjgjfcYGWNmiCCjdV QtaixAKNuyiZYgFdPgCSAE3GGRiGoYCe9pTSPanRIfiigKIk07ZPusJMI2rx xgD3lNKjTC9BeTddXVCYzGxmx/RVspWH2refqXHzyPvxUENEwO/xiY/Tsuqz suMXqGOB2GhSJcuybum80qO7Mm57C+KTHqamP4yNKwwJyw8KauTkNXF5j9jZ LTkFTzLznn5+4I/Ve+Qf75PN+Uxut1xuvURhvVDqML/c06tHDfFdJXBWCX/O +C+XQrngKr6zXeOzZvg+VZwHELGgeoTywa7uueuubAk2KUUjwkeZ0Eft+88R 50DFEKGhpQFlvkrJeCuZE5u64wfwFSofIzrF1zsiVR4JdxRav6D8STe7zp3r Zhe2J0ejf/AHQPDwQd9cRKmDoDiLlyG0vDuOog/KU+FVclRwxwfCTaYEFMr8 n8lRaB6CatN09foXC9AjV/Be9PARZSMNeo4JsiKaM0Ox+GRV1Jnkoe821KgD 5HNR9+UAPhzcKo8vasBHuG0JDATJTdT9WTN4if50FX3FAe+iyxdhD1vRTQaX mJ41QwYyeZLuEBhQ6M9ZUOS4YI+DaVRY44havMEkHELLs2Z4jaMf4QCPBVV8 wfN5S2WsqVK7RS8Xbm1fd+SRyy/5PxxsjPB/EhvXmpL+KJMbscCpYByLb2Ip mjND6PoF58bFvLAIcXxyfWp6fXJyXUxM2YOwvMDA+rSshoycxjROMze/NTPv 0X/2PV228/msTR32q6VWS2Rmc+TmMxQWs+QTpzVv/bqSncGkHn3vH+JAPp6I 6NxohN+r8R0UPeaIKBK6NOnM0jOqquqAFy5hHGHqD4G2A1EsEmGcSZ8SQ5bD hXfbHbR5M9QE3/QI8/l4igk3s2e78LEY7IJy8CHw58tgDgdpojEpRNeQqTMO ypdI4X96RKZ/lailm/J0J9MchYui/ANA6EcsGDj6JJbemak0MJCxNJY+B1G+ lm59dTKkcUpCpvf692a4fntjIIP2CBQOWj//smOC5Qsz+w6ruVIH5xeLdzSu OZh7dF9d6N3WqKjHcQlNySl+cx2TzCcWfrmae/7HnKAgUUx8dUKiKCauIjqm Njq66sGDsuBg7n2/h7GJDxPZkti0OnZOMzuvddOxp8572ud8/txmkdT8Q5mZ o3zCNIWxrcJ4svKJBoupTZ9uqggIFJWWUnRDczzUgnIUeKOW2iIFfYoFrwFd j9l2JqjRJWQ7npTQDsojGPTtoK8f9M02Gol3IKDUL1AOX13e7f5A3OvHny4W wDwMnuUelLH+XLEAf7Aa4q8QCyBKN2+VjjOWmlg+NTRvGm9TbzZbYr+Kt3Br 1hG3Kv+bDcGBDaGhteERwYvmp363I8v3ZnFQqCgiUhgeWRwWXhQaxgsOLggM LLp/n3f3Tuqtm+XBEcKY1LLI5MqkrMZk7vP1x54v2tFuvVxq+uFzm3mt67Y9 3n+08bRHw5Xr9ddvNnpcbtn//eNde+vOUn8yeNq2U0/1Dx/fx0LvxgSNsYCy Uec1A89aUKad+KXe8DksntKfwu7xnTmvFCAKwBoHRSvt2bM+yacko/B/Hhp3 Pb1O9Gkf0QA3h+Ni+xQLKO+gAEyIaBAVkZmQo4J24aIBsJ92+fhAgxgLXGhv cOq9/r1R+M2MBWI+v9Flp3S0XvtovWYd/VpdA/E408oJU/iWC7jzN7MPfyv0 vVJx20d8927F3bvsX37i3fIpuOdX6Ocn9A8QBgQU3L2bdutW0s2b4Ei/cSPj +vWYy5cKfe4JQuMFgTFVCRlNqdkvlu6S2q9qc97SePZKZRaXURVhOaUB/MxR zVHdRZV2oDTCMmVvuIUSC1AGA3DFUE0d4bvX1G/j6T5VVpYtOi/17y2pvXxn zmsG1GqwHA4rI/gBn4ODVylv23v96NM+osF6uXRfYwEaHZYs8as9xoIehQ8w FvR+oEGMBZRFgYh5G1X/8AbGgjqfuy8dZreN1qscz6qcZFNmaSOynsw3NM3V Mc4yskudtSZu6xf8O54lt31L/O6V3vcT+N8vDwoSx8RWZXCqc/Ml3LyatIyq 6LiywED2bd+YG54xntcjr1/NuOldFhYnikx6XF4lCY95OWXNHyu2iAXFg2V4 vwGJF88moULzEE4dXx3o9r4JgKn41/MOcBQphuqV40Pyzup+lA5fNQaXS+nQ YvJfwRsDsVFcUCD0uBS2YWPAvn25AYFlXK6wsFBUVCQqKChLSuKdv5D00epQ qwVBk6eyf/lRxMmqKytrEoubJNVNdfWPGpqaG1VHfcPj2vqW2rpHNbWNVTX1 5aLK0tIygaC8WNAkrnjyuLW5srJg9vJnJrNqb98fRMMJCP4sGPL/v4CAQDvK i4ryORx6Oyoll2Rnh9rM9dU3uG1sFD53Lm/95kK3E5n7T7L3Hc84cDz7yClw cA6dyHU7LNj1XdZ2t+RN38R/4Rqzcfcdp6UHpzlEzV+Yu3RNkdWcJvMZTwys qkPJf2FG8FcE/C8GhloLAoL+AIUD/9mOv777rzMjxwpt5sk2n355wKvu2C3h cW/hiZuiH33EP90S/ehddeTKHztPijYfzV13IH3992mrD+ev2ONtbLv5nbfL jFgS44l1hmaPdA0qfe8MtVkEBAQEBH1GcWrqiVEj3N9+98Jw/fYpzrLl+2Vb zj1zvfJ4v2fDYa8ad6+qIzcq3a/XHLjSvPlEw/rvK1YeKll7VLB8j8Dxy/Ip n0TomcWN1i0bZ1iuZ1Sto1d67MRQG0RAQEBA0EcIhYk//XT83Q8O/t/bybrj ZfYfyeZuki3fK/vsZ9n2Cy++vfJ07/W2vdceuV19vPvi75+ffLrm2O/Lv2te sf/h3M2Vk53LTGcUG1lmjtFLGT2mYIxe8Sjd4sXLROXUbUIEBAQEBG8yyoXC 7ISEI6N03P/x9gsTK/mkWbLJS2TT1ypmb1UsOSBf+4Ns028dm890bDn9cv0P L1cdaV+877mjS9usjU8sltRPW1ppO1swxpA7YnTsiFFxo3TYI3W5hsalmsoT BAQEBARvMtJDQjb+7e/JI0bJTSbKJ9gqTKfLbJ3anbf9sfXwi09c5bO2yRbv lS12kznt7nDc8Xzqhj+sVzw3mdN44ldxfoEIHIFBhavWJI8dF/De8Ij3R8Z+ MCrbq+e3DxEQEBAQvFG4fvDA4X/+U6GvrzAYL2dZtbl8I0lRvyJJXFLa6n5G YbtSPvU/8qmfdtiueG7u1G44/ffPvqII4cfExC9zvv7Ov/3+/X6E02KSJiIg ICD4E6FcKNxuZSkcMUqhp9f+oWNNVDS9T9s37grrJfJJ82TWTs+Mp7cbO1TH JWqUxr569byO7uVh71RpkkNAQEBA8GYiMynpxL/+pdDRa/n6G3H3Z7ERKvIL pbOXKV83ajb9hZHdkyWrRUIhk8CCpKRTxkaxM2aQpQEBAQHBnwW/bNvaNHJM ncdF7d3q7/grJtgpWA5SQ8um33p4ARqfw/nFwlx89drgqUlAQEBA8KrAZbOv vj+i6ezl3nT+Y8knCqOJcmOryti4HjsLcnKiXbZXcLMHrCMBAQEBwavF1W93 N+4/2svODVc9FcbWbVYOpTxeb/qX8HilJBYQEBAQvNnITE8XnPq19/3FZWUd 9rMfLVz66lQiICAgIHjNKC0o6Gt599mqTZyPh+z/jSIgICAg0Ij/B4IFulc= "], {{0, 0}, {516, 41}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {516, 41}, PlotRange -> {{0, 516}, {0, 41}}]], "DockedCell", Background -> GrayLevel[0.866682], CellFrame -> {{0, 0}, {0, 4}}, CellFrameColor -> RGBColor[0.690074, 0.12871, 0.194598], CellMargins -> {{0, 0}, {-3, 0}}, CellFrameMargins -> 0, ContextMenu -> None, ComponentwiseContextMenu -> {}], Cell[ BoxData[ GridBox[{{ GraphicsBox[ RasterBox[CompressedData[" 1:eJztWl1Ik1EYFrqNEoLMbHPmNkRrEhJERj93ra4cJvbDRIsyMk1pc03tTL1w aD+LfkQIJBkR/dBFdtHFDLywCykqoqgLIYRu6jbb8me933e+HT/P2fZN+sZ0 vg9n43zfec973nPe57zvOWNFDS2OhnU5OTlG+LyBj1S/ikAgEAgEAoFAIBAI xEpFMBh8jUgPYG0z7d7MAOYedm/Bko4Ca5tp92YGSCokle5AUiGpdAeSCkml O0RS/R1tjEajUIHvyIhdehPyLNZjrVSAgT5CK1Tmf32e+/qcdYEy+/4+vKTd oQJN89PjojbaHcrCzE8qn0RGfIxrEjcF0SomD49hYqDDUUSGKtUKWRMYz42L pFJDg1RPamGdlRWGuuDi2Yl+WHkoiy72W6jjgFeSm/wWKEAScCvtCxWpSzxt 1FPU9dJ76Lt8UnEmcVMQrWImUQE6nKJB7sgUKpb4LcpEtHiFpEpEKim2TI8n IhXv4pAHXCAJEAPIq7d5JFAOYYEGKHEstTbQAJKSx+XH5ZKKE+CmIFq1ZC/E SBVXoboJyMliKZKKgyapwLlK1ohHKgpYYfGRbnNpg4c8dP3prtckFQ0gUm5K miKpVZxnRZP4KcSziiU1bjhOobpJ2TtIqnhITipYZ7byydJfoDzMpT9ZWMo1 EHbgBBLyhOWzlmakUtKQnB/VuUYkFbWNjZXIJHEKnFVL0t+IXSQVU4iRKkUk JxVzhJI7hirpDpXOGzJ5eFLFvMNORxAlaJZhmtmZStQGAvSQA/FECSksH/kt VLMyokw5qHDOFU3ipiBaxZmtTSo8U2lBI1LF/BWNXZ0Y1LckLo9IqQdYIWdA 9T0uvPT2J2qjrUr2lGMRSzrq4eiIVIxFGC5bMZO4KYhWcWYnSn8gv3j7k+vJ GbVaSNXt9fo6O/XVib9Tpa+sClLdvtB0q+WSvjqRVGucVA/q6p9V1+irE0m1 xkk1cuLk2O49+upEUq1xUg1X14yZraSrS0ed+H+q9GFV/J+qx25/u9U40Nqa aUMQ2YMrFRWf8g0vDh9JvUvgYjPR+8KIyA5AyiNeb1Pe5ql840xxSV97eyq9 Hp1y3nE602waYoXC19GRqInIGHC57lY53Lm53/O2RQ3Fr6qqNXUG609/LLX1 ulOiHyL74D/XeLPxvPiexHDtsuulyexbv2GqwLRgNP8xl/W7XAQE1IUQ1nHw zNl5o2XYoc09RLbC5/E8te26V9+gfskY5SPkuss1abLc2Ljpm9E8Z7FFt++c POroJoQWn1wotQAPj9XMFZp/m6y9bndGpoNYCZBikbNuoqBwsPY4IxIrQJu+ trYf5pLRfOOXotJw6d7Zsv0LtkOPzzb1ENKjolagueVD5YGodUfEZH2372Cm p4X4X/wDFcRtOg== "], {{0, 0}, {199, 30}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {199, 30}, PlotRange -> {{0, 199}, {0, 30}}], ButtonBox[ GraphicsBox[ RasterBox[CompressedData[" 1:eJztlDFuhFAMRJHS5w45Re6RI+wFcoOUtNtR0lJSUlNSUtNS0m9JXjTKaPQh UfpgCeT1n2+Px15ebu9vt6eqqp55Xnm+/I/L/p+1bbtt277vvJumIcKbnwWs 73vBsHVdE1bXNQ55Ho8HMOEd3L9tWRZ+6tRBrrjEMAwigHO/37M6SII40zRB Q7QLkpQWjKOu63RqGHHVIoOYYAR16oucinYGxUo2jqMIzPNMnpQRPF2nMkeS cCBDXsm7ZNZp6oZRS3wsIBFNIYM2iY8gYmJA8imqawHcOAKqio4KSp4O7Qjp K1nOUygasaG2hoKSaud3krkArggZzyhhTohP3Uz7E0mNu9g98oj26exOSTon fRUtn8IUJL+W80gyuz6OW3mgrSXXEv5dSaRTaRz9KQpY/knxtVomKdFQxvFT JZFR6pFBJWT5tbEvR9+H3F6S+GOSMC+DTHtrHYyh32Qu855cdhn2CUundjY= "], {{0, 0}, {55, 14}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {55, 14}, PlotRange -> {{0, 55}, {0, 14}}], ButtonData -> { URL["http://store.wolfram.com/view/app/playerpro/"], None}, ButtonNote -> "http://store.wolfram.com/view/app/playerpro/"], GraphicsBox[ RasterBox[{{{132, 132, 132}, {156, 155, 155}}, {{138, 137, 137}, { 171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{ 138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, { 171, 169, 169}}, {{135, 135, 135}, {167, 166, 166}}}, {{0, 0}, {2, 14}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {2, 14}, PlotRange -> {{0, 2}, {0, 14}}], ButtonBox[ GraphicsBox[ RasterBox[CompressedData[" 1:eJztlSGSg2AMhTuzfu+wB1qzR+gF9gbIWhwSW4lEV1ZWYyvxSPZb3vAmDdDq zpCZdvKH5CUvfwhfx9+f48fhcPjk983vXy922eU9paqqcRx9HGcZhiE+PZ1O KHVd24KOgt0WFKLQ27ZdJrper0JGcS5CVqs6n89yRpGl73tZBK6kkvv97kCe ChOlLEvbVW2kiYPoxKcYRdwWld00jS2EcFSFMYXCqbOcBJzL5aJcxK7SFEFB GQFn8AWupPUkMRfIJEK53W5d1z2hGVP7yohVbfanWoxAJQTfeywbT1+xK9mi GQGTj8FT0uRAN3Tdjl3SlNANP5WoabIIRP+x52ojLEgXs8fxs7+R1cCXNFH6 SVJhKZwx0+BxBZ7nraGNpBSrEFlA1khgRDcCRg1navIWTeVKPVmliaeaL+c4 tCmcknRHfjtWaS6HNtYmC1wYjGJ+6eKjJcficWgVssz1nGbabFtD682gZaIO MHXqkq/vyW3GFaQXliNuOhbz9lOHU3a6SrhWkCmnXC9pUoPBt1aQpquYrtJt 0f6Pazkd497W1MkSlxierkrrN254iz8oHqS0ByzxGzfOHx2yq9plYSl8l13e Xf4ArlmHrg== "], {{0, 0}, {77, 14}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {77, 14}, PlotRange -> {{0, 77}, {0, 14}}], ButtonData -> { URL[ "http://www.wolfram.com/solutions/interactivedeployment/\ licensingterms.html"], None}, ButtonNote -> "http://www.wolfram.com/solutions/interactivedeployment/\ licensingterms.html"]}}, ColumnsEqual -> False, GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}]], "DockedCell", Background -> GrayLevel[0.494118], CellFrame -> {{0, 0}, {4, 0}}, CellFrameColor -> RGBColor[0.690074, 0.12871, 0.194598], CellMargins -> 0, CellFrameMargins -> {{0, 0}, {0, -1}}, ContextMenu -> None, ComponentwiseContextMenu -> {}, ButtonBoxOptions -> {ButtonFunction :> (FrontEndExecute[{ NotebookLocate[#2]}]& ), Appearance -> None, ButtonFrame -> None, Evaluator -> None, Method -> "Queued"}]}, FEPrivate`If[ FEPrivate`SameQ[ FrontEnd`CurrentValue[ FrontEnd`EvaluationNotebook[], ScreenStyleEnvironment], "SlideShow"], { Inherited}, {}]], Inherited], FrontEndVersion->"7.0 for Microsoft Windows (32-bit) (November 10, 2008)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[567, 22, 1310, 28, 150, "Section"], Cell[CellGroupData[{ Cell[1902, 54, 238, 3, 25, "Subsubsection"], Cell[2143, 59, 4691, 79, 133, "Input"], Cell[CellGroupData[{ Cell[6859, 142, 30512, 700, 19, "Input", CellOpen->False], Cell[37374, 844, 14703, 272, 659, "Output"] }, Open ]] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *) (* NotebookSignature cwDtrdYV1Tv9xBg8Ueh3kP4Q *)