§ Holonomic v/s non holonomic constraints

• A set of constraints such that the system under consideration becomes $TM$ where $M$ is the position space and $T_p M$ is the allowed velocities at position $p$ is a holonomic system
• A set of constraints such that the system under consideration cannot be thought of as $TM$ where $M$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