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§ Holonomic v/s Non Holonomic Constraints
created 2023-08-02
- A set of constraints such that the system under consideration becomes TM where M is the position space and TpM 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 Mis 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
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