Recent content by citheo

Ok, great! I'll try to solve some more problems like these on my own. Thanks for pointing me in the right direction, I really appreciate your help and patience!

Ah yes, I assume you mean \frac{d}{dt}(m\rho^2\dot{\theta}) = 0 \rightarrow \rho\cdot m\rho\dot{\theta} = \rho \cdot p_\theta = C, i.e. the angular momentum in the x-direction (or around the x-axis, whatever you call it..) is conserved. edit: So the conserved quantities/integrals of motion in...

Right, so it is explicitly independent of \theta and time. If I recall, a Lagrangian that doesn't change explicitly with time would mean that neither the kinetic term or the potential term changes explicitly with time, so the total energy is conserved? If we consider the system to be closed...

Oh okay, I was under the impression that an integral of motion would be an integration of the EOM's. In any case, the Lagrangian is as stated in #7. If I express x=x(\rho(t))\rightarrow dx/dt = \partial x / \partial \rho \cdot d\rho/dt I get L = \frac{1}{2}m(\dot{\rho}^2 + \rho^2\dot{\theta}^2...

Hm.. I can't seem to get anywhere with cylindrical coords. Whenever I try to calculate the total time derivative in EL eq. I tend to get terms with mixed time derivatives and of varying orders that I don't really know how to deal with. It doesn't seem to matter what substitution I make into L. : [

Cylindrical coords. would give me x=x,\ y = \rho cos\theta, z = \rho sin\theta where y^2+z^2 = \rho^2,\ -1<x<1,\ 0<\theta < 2\pi. The constraint would then become x^2 + 4\rho^2 = 1. The velocity squared for my mass is then v^2 = \rho^2 + \rho^2\dot{\theta}^2 + \dot{x}^2 which gives me L L =...

I'm going to go with what is cylindrical coordinates?

Oh right, I can just eliminate a variable straight away. Well, there is obviously some symmetry since the constraint can be thought of as a deformed sphere so some variant of spherical coordinates could perhaps work? I was thinking something like (2)-(5) here...

Homework Statement Suppose you have an object of mass m that is constrained to move on an ellipsoid with a constraint function f(x,y,z) = x^2+4y^2+4z^2 -1=0. Aside from the force of constraint, the only force acting on the mass is an elastic force \vec{F}=-kx\hat{x}. Find the Lagrangian, the...