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Math Help - Rotation of spiralling solution associate with complex eigenvalue of dynamical system

  1. #1
    Newbie erich22's Avatar
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    Rotation of spiralling solution associate with complex eigenvalue of dynamical system

    Hi, name is Eric. I'm a student in Indonesian university studying dynamical system.

    I'd like to ask sth concerning continuous dynamical system.

    If i have a planar autonomous or nonautonomous system, and the eigenvalue of the linearisation of the system is complex. Do the spiral of the solution in the phase portrait always rotate clockwise? Or can it rotate counterclockwise? Could u give me an example of dynamical system that rotate counterclockwise?

    Thank u very much 4 answering my question.

    GBU!
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  2. #2
    MHF Contributor
    Jester's Avatar
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    Clockwise

    \begin{array} {cl}<br />
\dot{x} &= y\\ <br />
\dot{y} &= -x<br />
\end{array}

    Counter-clockwise

    \begin{array} {cl}<br />
\dot{x} &= -y\\ <br />
\dot{y} &= x<br />
\end{array}
    Thanks from erich22
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