Suppose that g = g(q, p, t), and that H is the Hamiltonian. Show that: a) (See the Figure) b) if any quantity does not explicitly depend on time and its Poisson parenthesis with the Hamiltonian is null, such quantity is a constant of motion for the system.

Suppose that g = g(q, p, t), and that H is the Hamiltonian. Show that: a) (See the Figure) b) if any quantity does not explicitly depend on time and its Poisson parenthesis with the Hamiltonian is null, such quantity is a constant of motion for the system.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.CR: Chapter 6 Review

Problem 37CR

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Question

Suppose that g = g(q, p, t), and that H is the Hamiltonian. Show that:

a) (See the Figure)

b) if any quantity does not explicitly depend on time and its Poisson parenthesis with the Hamiltonian is null, such quantity is a constant of motion for the system.