Cartesian and Lagrangian Momentum
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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.
Key words:Descartes Lagrange momentum mechanics
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- 1.1. Abraham, R., and J. Marsden (1978), Foundations of Mechanics (Cambridge University of Press, Cambridge).Google Scholar
- 2.2. Descartes, R. (1647), Principes de la Philosophie (Henri le Gras, Paris).Google Scholar
- 3.3. Hermann, R. (1968), Differential Geometry and the Calculus of Variations (Academic, New York).Google Scholar
- 4.4. Lanczos, C. (1970), The Variational Principles of Mechanics (University of Toronto Press, Toronto).Google Scholar