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Bond Graph model

The schematic diagram of the system NonlinearMSD is displayed in Figure 4.1. The system comprises
The spring is unstretched when the rod makes an angle $ \theta = \alpa
= \frac{pi}{3}$ with the foundation.

Using elementary geometry, the effectice angular spring generates a torque $ \tau$ given by (4.1)

$\displaystyle \tau = -2kl^2 \cos{\frac{\theta}{2}} (\sin{\frac{\theta}{2}}-\sin{\frac{\alpha}{2}})$ (4.1)

The acausal bond graph of system NonlinearMSD is also displayed in Figure 4.1 (on page [*]). This shows the three bond graph components representing the friction R, the inertia I and the spring C components. The non-linear spring characteristic is given explicitly4.1.

The (nonlinear) system ordinary differential equation is given by MTT in Section [*] (on page [*]). This is a special case of the general non-linear ordinary differential equation:

\begin{displaymath}\begin{cases}\dot{x} = f(x,u)\\  y = g(x,u) \end{cases}\end{displaymath} (4.2)


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