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)
“Crime is naught but misdirected energy. So long as every institution of today, economic, political, social, and moral, conspires to misdirect human energy into wrong channels; so long as most people are out of place doing the things they hate to do, living a life they loathe to live, crime will be inevitable.”
—Emma Goldman (1869–1940)
“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)
“Each generation’s job is to question what parents accept on faith, to explore possibilities, and adapt the last generation’s system of values for a new age.”
—Frank Pittman (20th century)