Rocky Mountain Journal of Mathematics

The Differential Invariants of Particle Lagrangians under Equivalence by Contact Transformations

Michael D. Sutton

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Rocky Mountain J. Math., Volume 26, Number 1 (1996), 299-328.

First available in Project Euclid: 5 June 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53A55: Differential invariants (local theory), geometric objects
Secondary: 53B40: Finsler spaces and generalizations (areal metrics) 49J05: Free problems in one independent variable 70H99: None of the above, but in this section

Local differential invariants regular Lagrangian 1graphs contact transformations equivalent integrals Cartan's method of equivalence intrinsic calculations parametric calculations Finsler metric fundamental form structure equations Bianchi identities


Sutton, Michael D. The Differential Invariants of Particle Lagrangians under Equivalence by Contact Transformations. Rocky Mountain J. Math. 26 (1996), no. 1, 299--328. doi:10.1216/rmjm/1181072118.

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  • R. Bryant, On notions of equivalence for variational problems with one independent variable, Contemp. Math. 68 (1987), 65-76.
  • R. Bryant, S.S. Chern, R. Gardner, H. Goldschmidt and P. Griffiths, Exterior differential systems, Math. Sci. Res. Inst. Publ. 18 (1991).
  • R. Bryant and R. Gardner, Equivalence of particle Lagrangians under contact transformations, unpublished notes, 1979.
  • É. Cartan, Sur un problème d'équivalence et la théorie des espaces métriques généralisés, Mathematica 4 (1930), 114-136.
  • --------, Les sous-groupes des groupes continus de transformations, Ann. Éc. Normale 25 (1908), 57-194.
  • S. Chern, Local equivalence and Euclidean connections in Finsler spaces, Tsing Hua Univ. 5 (1948), 95-121.
  • --------, Pseudo groupes continus infinis, in Shiing-Shen Chern selected papers, Springer, New York, 1978.
  • R. Gardner, Differential geometric methods interfacing control theory, in Differential geometric control theory (R. Brockett et al., eds.), Birkhäuser, Boston, 1983.
  • --------, The method of equivalence and its applications, CBMS-NSF Regional Conf. Ser. Appl. Math. 58 (1989).
  • P. Griffiths, Exterior differential systems and the calculus of variations, Prog. Math. 25 (1983).
  • N. Kamran and P. Olver, Equivalence problems for first-order Lagrangians on the line, J. Differential Equations 80 (1989), 32-78.
  • N. Kamran and W. Shadwick, Cartan's method of equivalence and the classification of second-order differential equations, in Differential geometry: The interface between pure and applied mathematics (Mladen Luksic et al., eds.), Contem. Math. 68 (1987), 133-141.
  • P. Olver, Applications of Lie groups to differential equations, Grad. Texts Math. 107, Springer, New York, 1986.
  • H. Rund, The differential geometry of Finsler spaces, Springer, Berlin, 1959.
  • M. Spivak, A comprehensive introduction to differential geometry, Publish or Perish, Berkeley, 1979.
  • S. Sternberg, Lectures on differential geometry, Prentice-Hall, Englewood Cliffs, N.J., 1964.
  • M. Sutton, Equivalence of particle Lagrangians under contact transformations, Ph.D. dissertation, Chapel Hill, NC, 1988.
  • J. Wolf, Spaces of constant curvature, McGraw-Hill, New York, 1967.