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Alternative kinetic energy metrics for Lagrangian systems

Willy Sarlet UGent and G Prince (2010) JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 43(44).
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.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
INVERSE PROBLEM, SPHERICALLY SYMMETRIC-POTENTIALS, TANGENT BUNDLE, CALCULUS
journal title
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
J. Phys. A-Math. Theor.
volume
43
issue
44
article number
445204
pages
13 pages
Web of Science type
Article
Web of Science id
000283300800013
JCR category
PHYSICS, MULTIDISCIPLINARY
JCR impact factor
1.641 (2010)
JCR rank
23/79 (2010)
JCR quartile
2 (2010)
ISSN
1751-8113
DOI
10.1088/1751-8113/43/44/445204
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1088352
handle
http://hdl.handle.net/1854/LU-1088352
date created
2010-12-16 12:54:38
date last changed
2016-12-21 15:42:38
@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},
}

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.