Starting with an unconstrained mechanical system that is governed by an initial unconstrained Lagrangian, subsequently modified by nonholonomic, linear in velocities, constraints, an explicit construction for a Lagrangian that will produce mechanically correct equations of motion for that constrained nonholonomic system is given. Obtaining a Hamiltonian from that Lagrangian is briefly discussed.
Hebda, Piotr W. Ph.D. and Hebda, Beata Dr., "An explicit construction of mechanically correct Lagrangians for systems with linear nonholonomic constraints" (2020). Faculty Publications. 9.
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