Advanced search
2 files | 337.70 KB

Alternative kinetic energy metrics for Lagrangian systems

Willy Sarlet (UGent) and G Prince
Author
Organization
Abstract
We examine Lagrangian systems on R-n with standard kinetic energy terms for the possibility of additional, alternative Lagrangians with kinetic energy metrics different to the Euclidean one. Using the techniques of the inverse problem in the calculus of variations we find necessary and sufficient conditions for the existence of such Lagrangians. We illustrate the problem in two and three dimensions with quadratic and cubic potentials. As an aside we show that the well-known anomalous Lagrangians for the Coulomb problem can be removed by switching on a magnetic field, providing an appealing resolution of the ambiguous quantizations of the hydrogen atom.
Keywords
INVERSE PROBLEM, SPHERICALLY SYMMETRIC-POTENTIALS, TANGENT BUNDLE, CALCULUS

Downloads

  • (...).pdf
    • full text
    • |
    • UGent only
    • |
    • PDF
    • |
    • 168.75 KB
  • Kinetic energy metrics Sarlet Prince revised.pdf
    • full text
    • |
    • open access
    • |
    • PDF
    • |
    • 168.95 KB

Citation

Please use this url to cite or link to this publication:

Chicago
Sarlet, Willy, and G Prince. 2010. “Alternative Kinetic Energy Metrics for Lagrangian Systems.” Journal of Physics A-mathematical and Theoretical 43 (44).
APA
Sarlet, Willy, & Prince, G. (2010). Alternative kinetic energy metrics for Lagrangian systems. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 43(44).
Vancouver
1.
Sarlet W, Prince G. Alternative kinetic energy metrics for Lagrangian systems. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 2010;43(44).
MLA
Sarlet, Willy, and G Prince. “Alternative Kinetic Energy Metrics for Lagrangian Systems.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 43.44 (2010): n. pag. Print.
@article{1088352,
  abstract     = {We examine Lagrangian systems on R-n with standard kinetic energy terms for the possibility of additional, alternative Lagrangians with kinetic energy metrics different to the Euclidean one. Using the techniques of the inverse problem in the calculus of variations we find necessary and sufficient conditions for the existence of such Lagrangians. We illustrate the problem in two and three dimensions with quadratic and cubic potentials. As an aside we show that the well-known anomalous Lagrangians for the Coulomb problem can be removed by switching on a magnetic field, providing an appealing resolution of the ambiguous quantizations of the hydrogen atom.},
  articleno    = {445204},
  author       = {Sarlet, Willy and Prince, G},
  issn         = {1751-8113},
  journal      = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL},
  keyword      = {INVERSE PROBLEM,SPHERICALLY SYMMETRIC-POTENTIALS,TANGENT BUNDLE,CALCULUS},
  language     = {eng},
  number       = {44},
  pages        = {13},
  title        = {Alternative kinetic energy metrics for Lagrangian systems},
  url          = {http://dx.doi.org/10.1088/1751-8113/43/44/445204},
  volume       = {43},
  year         = {2010},
}

Altmetric
View in Altmetric
Web of Science
Times cited: