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## Homework Statement

A rod of length ##L## and mass ##M## is constrained to move in a vertical plane.

The upper end of the rod slides freely along a horizontal wire. Let ##x## be the

distance of the upper end of the rod from a fixed point, and let ##\theta## be the angle

between the rod and the downward vertical.

Show that the Lagrangian is $$L = \frac{1}{2}M \left(\dot{x}^2 + \frac{1}{3}L^2 \dot{\theta}^2 + L\dot{x}\dot{\theta} \cos \theta \right) + \frac{1}{2}MgL \cos \theta $$

## Homework Equations

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L = T - V

## The Attempt at a Solution

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I really can't make much sense out of the problem statement. I am picturing a rod fixed at the origin say, rotating in a vertical plane, thereby producing a cone shaped surface. I take 'upper part of rod' to mean like a bead attached to the rod, but not sure what it means to say it slides freely along a horizontal wire?

And the first term of the lagrangian is the kinetic energy of this 'bead' relative to the fixed point, but it gives it a mass M which I have understood to be the mass of the whole rod.

Many thanks for any clarity here!