Newtonian Dynamics - Kinetic Energy of A Constrained Newtonian Dynamical System

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:


T=\frac{1}{2}\sum^n_{i=1}\sum^n_{j=1}g_{ij}\,w^i\,w^j.

(12)

The formula (12) is derived by substituting (8) into (4) and taking into account (11).

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