# Foucault Pendulum - Lagrangian

1. Oct 27, 2007

### linm

1. The problem statement, all variables and given/known data
I should find the Lagrangian of a Foucault Pendulum in a coordinate system on the earth. That means L = T - V where T is the cinetic energy of the pendulum and V the potential energy.

2. Relevant equations

$$v' = v + [\omega, r]$$
[,] denotes the cross product

3. The attempt at a solution
I write the potential energy as
$$T = \frac{1}{2}mv'^2 = \frac{1}{2}m( (\dot{x}+ \dot{y} + \dot{z}) + \omega*sqrt(x^2+ y^2 + z^2)*sin(\phi))^2$$

where $$\phi$$ denotes the latitude.
The potential energy is given by
$$V = mgz$$
But when I solve this I get strange results. Does anyone see my problem. Thanks a lot for your help!