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(Solved): Write the equationu(t) + u(t) +u(t) cost = 0.as a matrix differential equation. Compute thei ...
Write the equation
u¨(t) + ?u(t) + u(t) cost = 0.
as a matrix differential equation. Compute the
i) monodromy matrix,
ii) characteristic multipliers,
and discuss the stability of the solutions.
![3. (4 points) Write the equation
\[
\ddot{u}(t)+\dot{u}(t)+u(t) \cos t=0 .
\]
as a matrix differential equation. Compute the](https://media.cheggcdn.com/media/33f/33feda22-e3b0-45a8-8df6-7963cb0cb72b/phpN71qKE)
3. (4 points) Write the equation \[ \ddot{u}(t)+\dot{u}(t)+u(t) \cos t=0 . \] as a matrix differential equation. Compute the i) monodromy matrix, ii) characteristic multipliers, and discuss the stability of the solutions.|
Expert Answer
Ans 1(I) The monodromy matrix \Phi can be calculated numerically by repeated integration of the systems equations \dot{y} = A(t) y over one period T, starting from independent sets of initial conditions. It is convenient to use the columns of the ide