- #1

eyenir

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## Homework Statement

a. Suppose two particles with mass $m$ and coordinates $x_1$, $x_2$ collides elastically, find the lagrangian and prove that the linear momentum is preserved.

b. Find new coordiantes (and lagrangian) s.t. the linear momentum is conjugate to the cyclical coordinate.

## Homework Equations

## The Attempt at a Solution

For (a) I thought that $L=m(\dot{x_1}^2+\dot{x_2}^2)/2$ but I don't know how to show the preservating of momentum.

For (b) I thought taking the new coordnates to be the center of mass and the distance of each particle from it but somehow I can't formulate it.

Can anybody assist with proving the momentum preservation and its conjugation in (b) for cyclical coordinates?