Answer to Question #302632 in Classical Mechanics for Sudhir

Question

Explain Hamilton's equation of motion in terms of Poisson's brackets.

Answer 1

Answer

set of first-order, highly symmetrical equations describing the motion of a classical dynamical system, namely

$q̇_j =\frac{ ∂ H }{∂ pj}\\, ṗ_j =\frac{ -∂ H }{∂ qj };$

here q_j (j = 1, 2,…) are generalized coordinates of the system, p_j is the momentum conjugate to q_j , and H is the Hamiltonian.

$[Q, P]=1$

For canonical.