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:
“All my stories are webs of style and none seems at first blush to contain much kinetic matter.... For me “style” is matter.”
—Vladimir Nabokov (1899–1977)
“Just as we are learning to value and conserve the air we breathe, the water we drink, the energy we use, we must learn to value and conserve our capacity for nurture. Otherwise, in the name of human potential we will slowly but surely erode the source of our humanity.”
—Elaine Heffner (20th century)
“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)
“New York is more now than the sum of its people and buildings. It makes sense only as a mechanical intelligence, a transporter system for the daily absorbing and nightly redeploying of the human multitudes whose services it requires.”
—Peter Conrad (b. 1948)