Cartesian and Lagrangian momentum

Afriat, Alexander (2006) Cartesian and Lagrangian momentum.

This is the latest version of this eprint.

Abstract

Historical, physical and geometrical relations between two different momenta, characterized here as Cartesian and Lagrangian, are explored. Cartesian momentum is determined by the mass tensor, and gives rise to a kinematical geometry. Lagrangian momentum, which is more general, is given by the fiber derivative, and produces a dynamical geometry. This differs from the kinematical in the presence of a velocity-dependent potential. The relation between trajectories and level surfaces in Hamilton-Jacobi theory can also be Cartesian and kinematical or, more generally, Lagrangian and dynamical.

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• Cartesian and Lagrangian momentum (deposited 06 April 2004)
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