Question

what are generalized coordiantes and generalised momentum? is this different from actual momentum? why it s termed as generalised?

Answer 1

Generalized coordinates are any coordinates which can uniquely describe the state of a physical system. Position of each particle in X,Y, and re generalized coordinates. They are the liar to students. When doing center-of-mass problems, the relative positions from the center of mass is easiest in terms of the equations of motion. Any coordinates which completely describe the system can be used. Angles are best used to describe peldula, so the GC do not even have to be positions. The generalized momentum the momentum of the GC. Actualy momentum is a generalized momentum, just like actualy position in a Generalized position. Usually, GC are used where you have as many variables as degrees of freesom, although when the DOF is greater, you can use Legrange Multipliers to make constraints amongst the variables.