Newton's third law, in not-necessarily-linear spaces
An extension is proposed for Newton's third law, the weak and strong forms, in not-necessarily linear spaces. This extension is based on the geodesic which connects two interacting particles. The result is that the forces that the two particles exert at each other have equal magnitudes; parallel-transported of one of these (along the connecting geodesic) from one particle to the other, is the negative of the other force; and in the strong form each force is tangent to the connecting geodesic. For forces derived from a potential energy, a form is proposed for the potential energy the forces corresponding to which satisfy the analog of the strong form of Newton's third law.
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