# 3D Motion/Precession/Stability of a rolling coin

1. Oct 25, 2009

### RollingCoin

1. The problem statement, all variables and given/known data

See the attached picture for the questions and information. This is actually due today and I haven't gotten all the answers - but it would be good to know how to do everything for when final exams come around. I particularly find (c), (d), (f), and (g) the most difficult.

2. Relevant equations

$$\dot{\psi}$$ = Precession rate
$$\dot{\theta}$$ = Nutation rate
$$p$$ = Spin

Angular momentum:
$$H_{x}=I_{x}\omega_{x}=I_{o}\dot{\theta}$$
$$H_{y}=I_{y}\omega_{y}=I_{o}\dot{\psi}sin\theta$$
$$H_{z}=I_{z}\omega_{z}=I\dot{\psi}cos\theta+p$$

Forced Precession:
$$M_{x}=\dot{\psi}sin\theta[I(\dot{\psi}cos\theta+p)-I_{o}(\dot{\psi}cos\theta)]$$

Free Precession:
$$\dot{\psi}=\frac{Ip}{(I_{o}-I)cos\theta}$$

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