§ Holonomic v/s non holonomic constraints
- A set of constraints such that the system under consideration becomes where is the position space and is the allowed velocities at position is a holonomic system
- A set of constraints such that the system under consideration cannot be thought of as where is the allowed positions. So we are imposing some artifical restrictions on the velocity of the system.
- Another restriction one often imposes is that constraint forces do no work.
- Under these assumptions, D'alambert's principle holds: the physical trajectory of the system is a constrained optimization problem: optimize the action functional of the free system restricted to paths lying on the constraint submanifold.
- Reference: SYMPLECTIC GEOMETRY AND HAMILTONIAN SYSTEMS by E Lerman