Yes, these all refer to the same concept.

[ehrenfest]

[SOLVED] classical mechanics

Homework Statement

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)?

Homework Equations

The Attempt at a Solution

 

[siddharth]

Homework Statement

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)?

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.