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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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.

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