Topic summary
Equation of motion
Extracted from the Wikipedia article Equations of motion.
Geodesic equation of motion
The above equations are valid in flat spacetime. In curvedspacetime, things become mathematically more complicated since there is no straight line; this is generalized and replaced by a geodesic of the curved spacetime (the shortest length of curve between two points). For curved manifolds with a metric tensorg, the metric provides the notion of arc length (see line element for details). The differential arc length is given by: