Foundations of Physics Letters

, Volume 18, Issue 4, pp 371–378 | Cite as

Cartesian and Lagrangian Momentum

  • Alexander Afriat
Original Article


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 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    1. Abraham, R., and J. Marsden (1978), Foundations of Mechanics (Cambridge University of Press, Cambridge).Google Scholar
  2. 2.
    2. Descartes, R. (1647), Principes de la Philosophie (Henri le Gras, Paris).Google Scholar
  3. 3.
    3. Hermann, R. (1968), Differential Geometry and the Calculus of Variations (Academic, New York).Google Scholar
  4. 4.
    4. Lanczos, C. (1970), The Variational Principles of Mechanics (University of Toronto Press, Toronto).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Istituto di FilosofiaUniversità di UrbinoUrbino

Personalised recommendations