Classical mechanics

1. Sep 21, 2007

ehrenfest

[SOLVED] classical mechanics

1. The problem statement, all variables and given/known data
is it true that conjugate momentum, canonical momentum, and generalized momentum all mean the same thing (the partial of the Lagrangian with respect to the time derivative of some generalized coordinate)?

2. Relevant equations

3. The attempt at a solution

2. Sep 21, 2007

siddharth

Yeah.

$$p_j = \frac{\partial L}{\partial \dot{q_j}}$$

is referred to as generalized momentum, canonical momentum or conjugate momentum.

Also, if the potential is velocity dependent, this generalized momentum will be different from the mechanical momentum of the system.