Newton's Second Law in A Curved Space
The Newtonian dynamical system (3) constrained to the configuration manifold by the constraint equations (6) is described by the differential equations
-
,
(15)
where are Christoffel symbols of the metric connection produced by the Riemannian metric (11).
Read more about this topic: Newtonian Dynamics
Famous quotes containing the words newton, law, curved and/or space:
“The next Augustan age will dawn on the other side of the Atlantic. There will, perhaps, be a Thucydides at Boston, a Xenophon at New York, and, in time, a Virgil at Mexico, and a Newton at Peru. At last, some curious traveller from Lima will visit England and give a description of the ruins of St. Pauls, like the editions of Balbec and Palmyra.”
—Horace Walpole (17171797)
“The older I get the more I trust in the law according to which the rose and the lily bloom.”
—Johann Wolfgang Von Goethe (17491832)
“By constant dripping, water hollows stone,
A signet-ring from use alone grows thin,
And the curved plowshare by soft earth is worn.”
—Ovid (Publius Ovidius Naso)
“As photographs give people an imaginary possession of a past that is unreal, they also help people to take possession of space in which they are insecure.”
—Susan Sontag (b. 1933)