Newtonian Dynamics - Newton's Second Law in A Curved Space

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

\frac{dq^s}{dt}=w^s,\qquad\frac{d w^s}{dt}+\sum^n_{i=1}\sum^n_{j=1}\Gamma^s_{ij}\,w^i\,w^j=F^s,\qquad s=1,\,\ldots,\,n,

(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:

    “Glorious things of thee are spoken, Zion city of our God!
    He, whose word cannot be broken, Form’d for thee his own abode:
    On the rock of ages founded, What can shake thy sure repose?
    With salvation’s walls surrounded Thou may’st smile at all thy foes.”
    —John Newton (1725–1807)

    “Laws can be wrong and laws can be cruel. And the people who live only by the law are both wrong and cruel.”
    —Ardel Wray. Mark Robson. Thea (Ellen Drew)

    “They are not flat surfaces
    Having curved outlines.
    They are round
    Tapering toward the top.”
    —Wallace Stevens (1879–1955)

    “Why not a space flower? Why do we always expect metal ships?”
    —W.D. Richter (b. 1945)