A particle of mass m described by one generalized coordinate q moves under the influence of a potential V(q) and a damping force −2mγq˙  proportional to its velocity. Show that the following Lagrangian gives the desired equation of motion: L = e2γt(1/2 * mq˙2 − V (q))

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A particle of mass m described by one generalized coordinate q moves
under the influence of a potential V(q) and a damping force −2mγq˙  proportional to its velocity. Show that the following Lagrangian gives the desired equation of motion:

L = e2γt(1/2 * mq˙2 − V (q))

 

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