(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A sphere of mass m2 and radius R rolls down a perfectly rough wedge of mass m1. The wedge sits on a frictionless surface so as the sphere rolls down, the wedge moves in opposite direction. Obtain the Lagrangian.

2. Relevant equations

3. The attempt at a solution

Here's my diagram of the situation. I used a cartesian system with the origin at the bottom corner of the wedge. Also I treated the sphere as the point in contact with the wedge, and I treat the wedge as a point at its top corner.

I imagined that as the sphere rolls down the incline, its y-value changes but the x-value stays the same as the wedge slips to the left (similar to someone slipping on a banana peel, or running on a free-floating log). Also, in an attempt to have x and y as my generalized coordinates, I expressed the distance [itex] s [/itex] the sphere makes along the incline in terms of x and y (see pic)

My Lagrangian worked out to be the following:

The problem I have with this is that if I were to continue finding equations of motion from this Lagrangian, I'd clearly have no equations to express the acceleration in the x-direction. I'm left with only acceleration in the y-direction but the wedge is clearly moving away from the origin so there should be x-acceleration there.

Should I be using a different point of origin? Or maybe a different coordinate system altogether??

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# Homework Help: Lagrangian of a sphere rolling down a moving incline

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