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Find the equations of motion for the Lagrangian L = eγt(mq˙2/2 − kq2/2) How would you describe the system? Are there any constants of motion?

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter1: Matrices, Vectors, And Vector Calculus

Section: Chapter Questions

Problem 1.3P

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Question

Find the equations of motion for the Lagrangian
L = e^γt(mq˙²/2 − kq²/2)
How would you describe the system? Are there any constants of motion?
Suppose a point transformation is made of the form
s = e^γt/2q.
What is the effective Lagrangian in terms of s? Find the equation of motion for s. What do these results say about the conserved quantities for the system?

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