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

A wedge of mass M and angle [alpha] slides freely on a horizontal plane. A particle of mass m moves freely on the wedge. Determine the motion of the particle as well as that of the wedge.

Note: We are supposed to use the Lagrangian formulation of mechanics to solve this problem.

3. The attempt at a solution

Okay, here's what I've got so far:

We can write the position of the mass m as

x = l cos [alpha];

y = l sin [alpha]

where l is the length of the hypotenuse of the wedge that the mass is sliding on.

Thus, the kintetic energy of the mass m is equal to [(1/2)m][l^2 cos^2(alpha) - l^2 sin^2(alpha)]; the potential energy is equal to [l sin(alpha)][mg]. Therefore, the Lagrangian can be written as

L = [(1/2)l^2m(cos^2(alpha) - sin^2(alpha))] - [l sin(alpha)][mg].

And that's as far as I've gotten; I'm having trouble with the rest. Help is appreciated greatly.

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# Homework Help: Help with Lagrangian problem

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