1. CARTESIAN AND LAGRANGIAN MOMENTUM.
- Author
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Afriat, Alexander
- Subjects
- *
MOMENTUM (Mechanics) , *LAGRANGIAN functions , *HAMILTON-Jacobi equations , *KINEMATICS , *DYNAMICS , *GEOMETRY - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2005
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