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).
Read more about this topic: Newtonian Dynamics
Famous quotes containing the words kinetic, energy, 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)
“The welfare, the happiness, the energy and spirit of the men and women who do the daily work ... is the underlying necessity of all prosperity.... There can be nothing wholesome unless their life is wholesome; there can be no contentment unless they are contented.”
—Woodrow Wilson (1856–1924)
“What a hell of an economic system! Some are replete with everything while others, whose stomachs are no less demanding, whose hunger is just as recurrent, have nothing to bite on. The worst of it is the constrained posture need puts you in. The needy man does not walk like the rest; he skips, slithers, twists, crawls.”
—Denis Diderot (1713–1784)
“If mothers are to be successful in achieving their child-rearing goals, they must have the inner freedom to find their own value system and within that system to find what is acceptable to them and what is not. This means leaving behind the anxiety, but also the security, of simplistic good-bad formulations and deciding for themselves what they want to teach their children.”
—Elaine Heffner (20th century)