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:
“Where the statue stood
Of Newton with his prism and silent face,
The marble index of a mind for ever
Voyaging through strange seas of thought, alone.”
—William Wordsworth (17701850)
“Jesus said to his Jews: The law was for servantslove God as I love him, as his son! What are morals to us sons of God!”
—Friedrich Nietzsche (18441900)
“They are not flat surfaces
Having curved outlines.
They are round
Tapering toward the top.”
—Wallace Stevens (18791955)
“Why not a space flower? Why do we always expect metal ships?”
—W.D. Richter (b. 1945)