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).

Read more about this topic:  Newtonian Dynamics

Famous quotes containing the words kinetic, constrained and/or system:

    “The poem has a social effect of some kind whether or not the poet wills it to have. It has kinetic force, it sets in motion ... [ellipsis in source] elements in the reader that would otherwise be stagnant.”
    —Denise Levertov (b. 1923)

    “An expansive life, one not constrained by four walls, requires as well an expansive pocket.”
    —Anton Pavlovich Chekhov (1860–1904)

    “We now come to the grand law of the system in which we are placed, as it has been developed by the experience of our race, and that, in one word, is SACRIFICE!”
    —Catherine E. Beecher (1800–1878)