Physics · Classical Mechanics
Suppose f, g are smooth functions of generalized coordinates q1, q2, ..., qn, the associated conjugate momenta p1, p2, ..., pn, and time t. Let [f, g] denote the Poisson bracket of f and g. Suppose H is the Hamiltonian of the system. Then which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1∂/∂t([f, g]) = [∂f/∂t, g] + [f, ∂g/∂t]
- 2If f is a constant of motion and independent of t, then [H, f] is a constant of motion
- 3[[H, f], g] + [[g, H], f] + [[f, g], H] = 0
- 4If f and g are constants of motion, then [f, g] is a constant of motion✓
Correct answer
If f and g are constants of motion, then [f, g] is a constant of motion
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