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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Modern Classical Mechanics

ISBN: 9781108834971

1st Edition

Authors: T. M. Helliwell, V. V. Sahakian

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Question Posted: Mar 16, 2024 11:27 AM

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Center of mass and relative coordinates. Show that for two particles moving in one dimension, with coordinates

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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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Modern Classical Mechanics

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