linm
Oct27-07, 03:22 PM
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!
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!