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Homework Help: Equations of motion for compound pendulum

  1. Jul 20, 2010 #1
    1. The problem statement, all variables and given/known data
    To derive the equations of motion for a compound pendulum. Pendulum parameters are: mass M, mass moment of inertia= Ixx,Iyy,Izz,Ixy,Iyz,Izx, Euler angles theta, phi & psi and their time-derivatives theta_dot, phi_dot, & psi_dot, and coordinates of center-of-mass (x,y,z)

    The coordinate system is give as; X & Y axis in horizontal plane, while Z axis point downwards. (SEE FIGURE attached with this post)

    2. Relevant equations
    Kinetic energy, T = 0.5 [tex]\omega * I * \omega[/tex]
    Potential energy, V = -m*g*z
    Lagrangian, L = T - V
    3. The attempt at a solution
    I have found the expression of c-o-m in terms of Euler angles:
    x = l*sin(theta)*cos(psi)
    y = l*sin(theta)*sin(psi)
    z = l*cos(theta)
    where, l is the distance between hinge point and c-o-m, and theta is inclination from Z axis, psi is angle between "l*sin(theta)" and X axis.

    Now, need to derive the expression for components of angular velocity in terms of Euler angles. How should I do that? Please help.
    Last edited: Jul 20, 2010
  2. jcsd
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