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:

    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 Paul’s, like the editions of Balbec and Palmyra.
    Horace Walpole (1717–1797)

    Law without education is a dead letter. With education the needed law follows without effort and, of course, with power to execute itself; indeed, it seems to execute itself.
    Rutherford Birchard Hayes (1822–1893)

    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)

    In the tale proper—where there is no space for development of character or for great profusion and variety of incident—mere construction is, of course, far more imperatively demanded than in the novel.
    Edgar Allan Poe (1809–1849)