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. If 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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- 1If f and g are constants of motion, then [f, g] is never a constant of motion
- 2[[H, f], g] + [[g, H], f] + [[f, g], H] = 1
- 3If f is a constant of motion, and f is independent of t, then [H, f] is a non-zero constant of motion
- 4∂∂t[f, g] = [∂f∂t, g] + [f, ∂g∂t]✓
Correct answer
∂∂t[f, g] = [∂f∂t, g] + [f, ∂g∂t]
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