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:

    “I frame no hypotheses; for whatever is not deduced from the phenomena is to be called a hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.”
    —Isaac Newton (1642–1727)

    “The law is simply expediency wearing a long white dress.”
    —Quentin Crisp (b. 1908)

    “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)

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