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).

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