Answered: Verify that the Hamiltonian equation…

Verify that the Hamiltonian equation H(x, p, t) = T + V = p2/2m + (k/2) (x − v0t)2 leads to the same motion as described by the following equation: mx¨'= −kx', where x' = x − v0t.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics

Section: Chapter Questions

Problem 7.26P

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Question

Verify that the Hamiltonian equation
H(x, p, t) = T + V = p²/2m + (k/2) (x − v₀t)²
leads to the same motion as described by the following equation:
mx¨'= −kx', where x' = x − v₀t.

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