11 lines
591 B
Markdown
11 lines
591 B
Markdown
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PROBLEM
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A system consists of one particle of mass M and n particles with equal masses m. Eliminate
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the motion of the centre of mass and so reduce the problem to one involving n particles.
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SOLUTION. Let R be the radius vector of the particle of mass M, and Ra (a = 1, 2, ..., n)
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those of the particles of mass m. We put ra = Ra-R and take the origin to be at the centre
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of mass: MR+mER = 0. Hence where =M + nm; Ra = R + ra.
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Substitution in the Lagrangian L = gives
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ra.
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The potential energy depends only on the distances between the particles, and so can be
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written as a function of the ra.
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