Center of mass and relative coordinates. Show that for two particles moving in one dimension, with coordinates
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Center of mass and relative coordinates. Show that for two particles moving in one dimension, with coordinates \(x_{1}\) and \(x_{2}\), with a potential that depends only upon their separation \(x_{2}-x_{1}\), then the Lagrangian
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can be rewritten in the form 1 L = mx + mx - U(x2 x1) - L = 1 = x + x - U(x), where Mm + m2 is the total mass and = m1m2/M is the "reduced mass" of the system, and X (mx+m2x2)/M is the center of mass coordinate and x' = x2-x is the relative coordinate. =
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