# Homework Help: A box on a moving wedge, on an inclined plane

1. Apr 29, 2012

### Demon117

1. The problem statement, all variables and given/known data
The situation is indicated in the diagram below. Block m is at rest, and the block M has an initial velocity upward. Need to find the Lagrangian of this system, and then the Euler-Lagrange equations.

3. The attempt at a solution

This is the Lagrange that I came up with from the beginning, but it seems like I am oversimplifying it:

$T=(1/2)m(\dot{x_{1}}^{2}+\dot{y_{1}}^{2})+(1/2)M(\dot{x_{2}}^{2}+\dot{y_{2}}^{2})$

$V= mgy_{1}cos(\beta) + Mgy_{2}cos(\alpha)$

$L=(1/2)m(\dot{x_{1}}^{2}+\dot{y_{1}}^{2})+(1/2)M(\dot{x_{2}}^{2}+\dot{y_{2}}^{2}) - mgy_{1}cos(\beta) - Mgy_{2}cos(\alpha)$

Like I said, this seems over simplified and I feel like there should be some cross terms in the kinetic energies. The second attempt that I have made is try to come up with velocity vectors. In this case I have the velocity of the wedge with respect to the incline $v_{w}=\left(\partial _tx_2\right)\hat{i}-\left(\partial _ty_2\right)\hat{j}$ and the velocity of the box with respect to the wedge, with respect to the incline $v_{B}=\left(\partial _tx_2\right)\hat{i}-\left(\partial _ty_2\right)\hat{j}+\left(\partial _tx_1\right)\hat{i}'-\left(\partial _ty_1\right)\hat{j}'$.

Geometry has always been an extreme weakness of mine. It seems like I am approaching this in all of the wrong ways. Any suggestions would be helpful.

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Last edited: Apr 29, 2012
2. May 2, 2012

### dikmikkel

You have to write your generalized coordinates at first, then you would have some cos sine dependence in the velocity. That is because the box is constrained to move in a certain way and by not introducing gen. coordinates you would simply get newtons 2nd law.
Also your potential energies have different zero points?
Define a coordinate system