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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?