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Well, I’ve got a problem to solve but I’m not gonna ask you to do it for me. Instead, what I need is an explanation of what I am doing wrong.

The problem is as follows: we have a rod of mass m and length l hanging of a rail (don’t know how to call it). It moves as the diagram shows,. I am asked (using Lagrangian mechanics) to write down the movement equations. And once done so, imagine theta is constant, what is the equation of just the translation motion?

The generalized coordinates I take are q and theta (alpha is fixed) and therefore the positions of the centre of mass of the rod is:

X=qcos(alpha)-L/2sin(theta)

Y= qsin(alpha)-L/2cos(theta)

Now I write the Lagrangian (taking into account that the kinetic energy of the rod is the T of the center of mass plus the kinetic energy around the center of mass).

Well, after cancelling all theta’s derivatives (cause theta is constant) I reach to this conclusion:

1.equation mq’’=-mgsin(alpha)

2. equation mq’’=g sin(theta)/cos(alpha+theta)

Equation 1 makes sense, but the second doesn’t. That’s why I think I’m doing something wrong. Please help!

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# Homework Help: Lagrangian mechanics (problem with generalized coordinates)

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