Two particles of equal masses m1=m2 move on a frictionless horizontal surface in the vicinity of...

Two particles of equal masses m1=m2 move on a frictionless horizontal surface in the vicinity of a fixed force center, with potential energies U1 = 1/2kr^(2)1 and U2 = 1/2kr^(2)2. In addition they interact with each other via a potential energy U12 = 1/2αkr^2 where r is the distance between them and α and k are positive constants.

(a) Find the Lagrangian in terms of the CM position R and the relative position r.

(b) Write down and solve the Euler-Lagrange equations for the CM and relative coordinates X, Y and x, y. Describe the motion.

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genius_generous answered 1 year ago

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