8.8** Two masses m₁ and m₂ move in a plane and interact by a potential energy U(r) = kr². Write down their Lagrangian in terms of the CM and relative positions R and r, and find the equations of motion for the coordinates X, Y and x, y. Describe the motion and find the frequency of the relative motion.
8.8** Two masses m₁ and m₂ move in a plane and interact by a potential energy U(r) = kr². Write down their Lagrangian in terms of the CM and relative positions R and r, and find the equations of motion for the coordinates X, Y and x, y. Describe the motion and find the frequency of the relative motion.
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This is question 8.8 in John R. Taylor's "
Transcribed Image Text:8.8** Two masses m₁ and m₂ move in a plane and interact by a potential energy U(r) = kr². Write
down their Lagrangian in terms of the CM and relative positions R and r, and find the equations of
motion for the coordinates X, Y and x, y. Describe the motion and find the frequency of the relative
motion.
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