Kinetic Energy of A Constrained Newtonian Dynamical System
Since the Euclidean structure of an unconstrained system of particles is entroduced through their kinetic energy, the induced Riemannian structure on the configuration space of a constrained system preserves this relation to the kinetic energy:
-
.(12)
The formula (12) is derived by substituting (8) into (4) and taking into account (11).
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