Physics Notes - Herong's Tutorial Notes - v3.24, by Herong Yang
Relation of Momentum and Hamiltonian
This section describes the Relation of Momentum and Hamiltonian.
Hamiltonian, H, is related to momentum, p, through the kinetic energy, T.
Let's use a single object as an example:
H = T + V (H.1) or: H = 0.5*m*v*v + V # Since T = 0.5*m*v*v or: H = 0.5*p*v + V # p = m*v applied or: H = 0.5*p*p/m + V # p = m*v applied again
If we apply the law of conservation of energy, we can have:
H = constant T + V = constant (H.2) or: dH/dt = 0 dT/dt + dV/dt = 0 dT/dt = -dV/dt (H.3) or: d(0.5*p*p/m)/dt = - dV/dt p*p'/m = -dV/dt or: v*p' = -dV/dt # p = m*v applied
Table of Contents