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3D Motion/Precession/Stability of a rolling coin

  1. Oct 25, 2009 #1
    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

    [tex]\dot{\psi}[/tex] = Precession rate
    [tex]\dot{\theta}[/tex] = Nutation rate
    [tex]p[/tex] = Spin

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

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

    Free Precession:
    [tex]\dot{\psi}=\frac{Ip}{(I_{o}-I)cos\theta}[/tex]
     

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