# Homework Help: Equations of motion for compound pendulum

1. Jul 20, 2010

### msntito

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)
https://www.physicsforums.com/attachment.php?attachmentid=27054&stc=1&d=1279608886

2. Relevant equations
Kinetic energy, T = 0.5 $$\omega * I * \omega$$
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