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Math Help - direction field and trajectories

  1. #1
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    direction field and trajectories

    Could someone please explain how you draw the direction field and plot a few trajectories of a system. An example would be

    x'= {3 -2 } x
    {2 -2 }

    In brackets is a 2 by 2 matrix if its not obvious. Any help appreciated greatly.
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  2. #2
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    Quote Originally Posted by ur5pointos2slo View Post
    Could someone please explain how you draw the direction field and plot a few trajectories of a system. An example would be

    x'= {3 -2 } x
    {2 -2 }

    In brackets is a 2 by 2 matrix if its not obvious. Any help appreciated greatly.
    X'= \begin{bmatrix}3 & -2 \\ 2 & -2\end{bmatrix}X

    or, if X'= \begin{bmatrix}x \\ y\end{bmatrix},
    \begin{bmatrix}x' \\ y'\end{bmatrix}= \begin{bmatrix}3 & -2 \\ 2 & -2\end{bmatrix}\begin{bmatrix}x \\ y\end{bmatrix}

    which is the same as the system of equations, x'= 3x- 2y, y'= 2x- 2y.

    For a number of different points (x,y), calculate x' and y' and, at that point, draw a short vector with slope y'/x'. That's the "direction field". A "trajectory" is a continuous curve that is parallel to the direction field vectors at each point.
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