untitled-3.nb

该程序是用来画微分系统时间序列图相图等相关的图形的,可以很好的对一个微分系统进行分析

        0, \(35\ w\ \((x - \(35\ z\)\/\(k\^2 + w\^2\))\)\)\/\(\((k\^2 + w\^2)\
\)\ \((w\/35 + \(35\ w\)\/\(k\^2 + w\^2\))\)\) + \(w\ \((kz\/\(k\^2 + w\^2\) \
- wy\/35 + x)\)\ k\_1\)\/\(\((k\^2 + w\^2)\)\ \((w\/35 + \(35\ w\)\/\(k\^2 + \
w\^2\))\)\), 0}, {0, 
        0, \(\((\(-1\) + \(35\ k\)\/\(k\^2 + w\^2\))\)\ \((x - \(35\ z\)\/\(k\
\^2 + w\^2\))\)\)\/\(w\/35 + \(35\ w\)\/\(k\^2 + w\^2\)\) + \(\((35\/\(k\^2 + \
w\^2\) + k\/\(k\^2 + w\^2\))\)\ \((kz\/\(k\^2 + w\^2\) - wy\/35 + x)\)\ \
k\_1\)\/\(w\/35 + \(35\ w\)\/\(k\^2 + w\^2\)\), 0}, {0, 
        0, \(w\ \((x - \(35\ z\)\/\(k\^2 + w\^2\))\)\)\/\(w\/35 + \(35\ w\)\/\
\(k\^2 + w\^2\)\) + \(w\ \((kz\/\(k\^2 + w\^2\) - wy\/35 + x)\)\ k\_1\)\/\(35\
\ \((w\/35 + \(35\ w\)\/\(k\^2 + w\^2\))\)\), 
        0}, {0, \(-x\) + \(35\ z\)\/\(k\^2 + w\^2\), 0, 0}}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{\(l = {{0, 
          0, \(35\ w\ \((x - \(35\ z\)\/\(k\^2 + w\^2\))\)\)\/\(\((k\^2 + \
w\^2)\)\ \((w\/35 + \(35\ w\)\/\(k\^2 + w\^2\))\)\) + \(w\ \((kz\/\(k\^2 + \
w\^2\) - wy\/35 + x)\)\ k\_1\)\/\(\((k\^2 + w\^2)\)\ \((w\/35 + \(35\ \
w\)\/\(k\^2 + w\^2\))\)\), 0}, {0, 
          0, \(\((\(-1\) + \(35\ k\)\/\(k\^2 + w\^2\))\)\ \((x - \(35\ \
z\)\/\(k\^2 + w\^2\))\)\)\/\(w\/35 + \(35\ w\)\/\(k\^2 + w\^2\)\) + \(\((35\/\
\(k\^2 + w\^2\) + k\/\(k\^2 + w\^2\))\)\ \((kz\/\(k\^2 + w\^2\) - wy\/35 + x)\
\)\ k\_1\)\/\(w\/35 + \(35\ w\)\/\(k\^2 + w\^2\)\), 0}, {0, 
          0, \(w\ \((x - \(35\ z\)\/\(k\^2 + w\^2\))\)\)\/\(w\/35 + \(35\ w\)\
\/\(k\^2 + w\^2\)\) + \(w\ \((kz\/\(k\^2 + w\^2\) - wy\/35 + x)\)\ \
k\_1\)\/\(35\ \((w\/35 + \(35\ w\)\/\(k\^2 + w\^2\))\)\), 
          0}, {0, \(-x\) + \(35\ z\)\/\(k\^2 + w\^2\), 0, 
          0}}\), "\[IndentingNewLine]", 
    RowBox[{"p", "=", 
      RowBox[{"(", GridBox[{
            {"1", "0", \(\(-35\)\/\(w\^2 + k\^2\)\), "0"},
            {"1", \(-\(w\/35\)\), \(k\/\(w^2 + k^2\)\), "0"},
            {"0", "0", "0", "1"},
            {\(-k\), "w", "1", "0"}
            }], ")"}]}], "\[IndentingNewLine]", \(B = l . p\)}], "Input"],

Cell[BoxData[
    \({{0, 
        0, \(35\ w\ \((x - \(35\ z\)\/\(k\^2 + w\^2\))\)\)\/\(\((k\^2 + w\^2)\
\)\ \((w\/35 + \(35\ w\)\/\(k\^2 + w\^2\))\)\) + \(w\ \((kz\/\(k\^2 + w\^2\) \
- wy\/35 + x)\)\ k\_1\)\/\(\((k\^2 + w\^2)\)\ \((w\/35 + \(35\ w\)\/\(k\^2 + \
w\^2\))\)\), 0}, {0, 
        0, \(\((\(-1\) + \(35\ k\)\/\(k\^2 + w\^2\))\)\ \((x - \(35\ z\)\/\(k\
\^2 + w\^2\))\)\)\/\(w\/35 + \(35\ w\)\/\(k\^2 + w\^2\)\) + \(\((35\/\(k\^2 + \
w\^2\) + k\/\(k\^2 + w\^2\))\)\ \((kz\/\(k\^2 + w\^2\) - wy\/35 + x)\)\ \
k\_1\)\/\(w\/35 + \(35\ w\)\/\(k\^2 + w\^2\)\), 0}, {0, 
        0, \(w\ \((x - \(35\ z\)\/\(k\^2 + w\^2\))\)\)\/\(w\/35 + \(35\ w\)\/\
\(k\^2 + w\^2\)\) + \(w\ \((kz\/\(k\^2 + w\^2\) - wy\/35 + x)\)\ k\_1\)\/\(35\
\ \((w\/35 + \(35\ w\)\/\(k\^2 + w\^2\))\)\), 
        0}, {0, \(-x\) + \(35\ z\)\/\(k\^2 + w\^2\), 0, 0}}\)], "Output"],

Cell[BoxData[
    \({{1, 0, \(-\(35\/\(k\^2 + w\^2\)\)\), 0}, {1, \(-\(w\/35\)\), 
        k\/\(k\^2 + w\^2\), 0}, {0, 0, 0, 1}, {\(-k\), w, 1, 0}}\)], "Output"],

Cell[BoxData[
    \({{0, 0, 
        0, \(35\ w\ \((x - \(35\ z\)\/\(k\^2 + w\^2\))\)\)\/\(\((k\^2 + w\^2)\
\)\ \((w\/35 + \(35\ w\)\/\(k\^2 + w\^2\))\)\) + \(w\ \((kz\/\(k\^2 + w\^2\) \
- wy\/35 + x)\)\ k\_1\)\/\(\((k\^2 + w\^2)\)\ \((w\/35 + \(35\ w\)\/\(k\^2 + \
w\^2\))\)\)}, {0, 0, 
        0, \(\((\(-1\) + \(35\ k\)\/\(k\^2 + w\^2\))\)\ \((x - \(35\ z\)\/\(k\
\^2 + w\^2\))\)\)\/\(w\/35 + \(35\ w\)\/\(k\^2 + w\^2\)\) + \(\((35\/\(k\^2 + \
w\^2\) + k\/\(k\^2 + w\^2\))\)\ \((kz\/\(k\^2 + w\^2\) - wy\/35 + x)\)\ \
k\_1\)\/\(w\/35 + \(35\ w\)\/\(k\^2 + w\^2\)\)}, {0, 0, 
        0, \(w\ \((x - \(35\ z\)\/\(k\^2 + w\^2\))\)\)\/\(w\/35 + \(35\ w\)\/\
\(k\^2 + w\^2\)\) + \(w\ \((kz\/\(k\^2 + w\^2\) - wy\/35 + x)\)\ k\_1\)\/\(35\
\ \((w\/35 + \(35\ w\)\/\(k\^2 + w\^2\))\)\)}, {\(-x\) + \(35\ z\)\/\(k\^2 + \
w\^2\), \(-\(1\/35\)\)\ w\ \((\(-x\) + \(35\ z\)\/\(k\^2 + w\^2\))\), \(k\ \
\((\(-x\) + \(35\ z\)\/\(k\^2 + w\^2\))\)\)\/\(k\^2 + w\^2\), 0}}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{\(h = {{0, 0, 
          0, \(35\ w\ \((x - \(35\ z\)\/\(k\^2 + w\^2\))\)\)\/\(\((k\^2 + \
w\^2)\)\ \((w\/35 + \(35\ w\)\/\(k\^2 + w\^2\))\)\) + \(w\ \((kz\/\(k\^2 + \
w\^2\) - wy\/35 + x)\)\ k\_1\)\/\(\((k\^2 + w\^2)\)\ \((w\/35 + \(35\ \
w\)\/\(k\^2 + w\^2\))\)\)}, {0, 0, 
          0, \(\((\(-1\) + \(35\ k\)\/\(k\^2 + w\^2\))\)\ \((x - \(35\ \
z\)\/\(k\^2 + w\^2\))\)\)\/\(w\/35 + \(35\ w\)\/\(k\^2 + w\^2\)\) + \(\((35\/\
\(k\^2 + w\^2\) + k\/\(k\^2 + w\^2\))\)\ \((kz\/\(k\^2 + w\^2\) - wy\/35 + x)\
\)\ k\_1\)\/\(w\/35 + \(35\ w\)\/\(k\^2 + w\^2\)\)}, {0, 0, 
          0, \(w\ \((x - \(35\ z\)\/\(k\^2 + w\^2\))\)\)\/\(w\/35 + \(35\ w\)\
\/\(k\^2 + w\^2\)\) + \(w\ \((kz\/\(k\^2 + w\^2\) - wy\/35 + x)\)\ \
k\_1\)\/\(35\ \((w\/35 + \(35\ w\)\/\(k\^2 + w\^2\))\)\)}, {\(-x\) + \(35\ \
z\)\/\(k\^2 + w\^2\), \(-\(1\/35\)\)\ w\ \((\(-x\) + \(35\ z\)\/\(k\^2 + w\^2\
\))\), \(k\ \((\(-x\) + \(35\ z\)\/\(k\^2 + w\^2\))\)\)\/\(k\^2 + w\^2\), 
          0}}\), "\[IndentingNewLine]", 
    RowBox[{"g", "=", 
      RowBox[{"(", GridBox[{
            {"x"},
            {"y"},
            {"z"},
            {"w"}
            }], ")"}]}], "\[IndentingNewLine]", \(h . g\)}], "Input"],

Cell[BoxData[
    \({{0, 0, 
        0, \(35\ w\ \((x - \(35\ z\)\/\(k\^2 + w\^2\))\)\)\/\(\((k\^2 + w\^2)\
\)\ \((w\/35 + \(35\ w\)\/\(k\^2 + w\^2\))\)\) + \(w\ \((kz\/\(k\^2 + w\^2\) \
- wy\/35 + x)\)\ k\_1\)\/\(\((k\^2 + w\^2)\)\ \((w\/35 + \(35\ w\)\/\(k\^2 + \
w\^2\))\)\)}, {0, 0, 
        0, \(\((\(-1\) + \(35\ k\)\/\(k\^2 + w\^2\))\)\ \((x - \(35\ z\)\/\(k\
\^2 + w\^2\))\)\)\/\(w\/35 + \(35\ w\)\/\(k\^2 + w\^2\)\) + \(\((35\/\(k\^2 + \
w\^2\) + k\/\(k\^2 + w\^2\))\)\ \((kz\/\(k\^2 + w\^2\) - wy\/35 + x)\)\ \
k\_1\)\/\(w\/35 + \(35\ w\)\/\(k\^2 + w\^2\)\)}, {0, 0, 
        0, \(w\ \((x - \(35\ z\)\/\(k\^2 + w\^2\))\)\)\/\(w\/35 + \(35\ w\)\/\
\(k\^2 + w\^2\)\) + \(w\ \((kz\/\(k\^2 + w\^2\) - wy\/35 + x)\)\ k\_1\)\/\(35\
\ \((w\/35 + \(35\ w\)\/\(k\^2 + w\^2\))\)\)}, {\(-x\) + \(35\ z\)\/\(k\^2 + \
w\^2\), \(-\(1\/35\)\)\ w\ \((\(-x\) + \(35\ z\)\/\(k\^2 + w\^2\))\), \(k\ \
\((\(-x\) + \(35\ z\)\/\(k\^2 + w\^2\))\)\)\/\(k\^2 + w\^2\), 0}}\)], "Output"],

Cell[BoxData[
    \({{x}, {y}, {z}, {w}}\)], "Output"],

Cell[BoxData[
    \({{w\ \((\(35\ w\ \((x - \(35\ z\)\/\(k\^2 + w\^2\))\)\)\/\(\((k\^2 + \
w\^2)\)\ \((w\/35 + \(35\ w\)\/\(k\^2 + w\^2\))\)\) + \(w\ \((kz\/\(k\^2 + \
w\^2\) - wy\/35 + x)\)\ k\_1\)\/\(\((k\^2 + w\^2)\)\ \((w\/35 + \(35\ \
w\)\/\(k\^2 + w\^2\))\)\))\)}, {w\ \((\(\((\(-1\) + \(35\ k\)\/\(k\^2 + \
w\^2\))\)\ \((x - \(35\ z\)\/\(k\^2 + w\^2\))\)\)\/\(w\/35 + \(35\ \
w\)\/\(k\^2 + w\^2\)\) + \(\((35\/\(k\^2 + w\^2\) + k\/\(k\^2 + w\^2\))\)\ \
\((kz\/\(k\^2 + w\^2\) - wy\/35 + x)\)\ k\_1\)\/\(w\/35 + \(35\ w\)\/\(k\^2 + \
w\^2\)\))\)}, {w\ \((\(w\ \((x - \(35\ z\)\/\(k\^2 + w\^2\))\)\)\/\(w\/35 + \
\(35\ w\)\/\(k\^2 + w\^2\)\) + \(w\ \((kz\/\(k\^2 + w\^2\) - wy\/35 + x)\)\ k\
\_1\)\/\(35\ \((w\/35 + \(35\ w\)\/\(k\^2 + w\^2\))\)\))\)}, {x\ \((\(-x\) + \
\(35\ z\)\/\(k\^2 + w\^2\))\) - 
          1\/35\ w\ y\ \((\(-x\) + \(35\ z\)\/\(k\^2 + w\^2\))\) + \(k\ z\ \
\((\(-x\) + \(35\ z\)\/\(k\^2 + w\^2\))\)\)\/\(k\^2 + w\^2\)}}\)], "Output"]
}, Open  ]]
},
FrontEndVersion->"5.0 for Microsoft Windows",
ScreenRectangle->{{0, 1280}, {0, 877}},
WindowSize->{1272, 843},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
Magnification->2
]

(*******************************************************************
Cached data follows.  If you edit this Notebook file directly, not
using Mathematica, you must remove the line containing CacheID at
the top of  the file.  The cache data will then be recreated when
you save this file from within Mathematica.
*******************************************************************)

(*CellTagsOutline
CellTagsIndex->{}
*)

(*CellTagsIndex
CellTagsIndex->{}
*)

(*NotebookFileOutline
Notebook[{

Cell[CellGroupData[{
Cell[1776, 53, 448, 10, 325, "Input"],
Cell[2227, 65, 161, 2, 99, "Output"],
Cell[2391, 69, 68, 1, 99, "Output"],
Cell[2462, 72, 728, 11, 310, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[3227, 88, 1080, 19, 556, "Input"],
Cell[4310, 109, 161, 2, 99, "Output"],
Cell[4474, 113, 775, 12, 309, "Output"],
Cell[5252, 127, 1969, 32, 736, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[7258, 164, 1182, 19, 584, "Input"],
Cell[8443, 185, 728, 11, 310, "Output"],
Cell[9174, 198, 214, 3, 156, "Output"],
Cell[9391, 203, 853, 13, 307, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[10281, 221, 1202, 20, 558, "Input"],
Cell[11486, 243, 853, 13, 307, "Output"],
Cell[12342, 258, 161, 2, 99, "Output"],
Cell[12506, 262, 971, 14, 381, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[13514, 281, 1198, 21, 603, "Input"],
Cell[14715, 304, 971, 14, 381, "Output"],
Cell[15689, 320, 54, 1, 80, "Output"],
Cell[15746, 323, 962, 13, 385, "Output"]
}, Open  ]]
}
]
*)



(*******************************************************************
End of Mathematica Notebook file.
*******************************************************************)