The Regularization of the Second Order Lagrangians in Example

Dana Smetanová

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2016)

  • Volume: 55, Issue: 2, page 157-165
  • ISSN: 0231-9721

Abstract

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This paper is devoted to geometric formulation of the regular (resp. strongly regular) Hamiltonian system. The notion of the regularization of the second order Lagrangians is presented. The regularization procedure is applied to concrete example.

How to cite

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Smetanová, Dana. "The Regularization of the Second Order Lagrangians in Example." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 55.2 (2016): 157-165. <http://eudml.org/doc/287887>.

@article{Smetanová2016,
abstract = {This paper is devoted to geometric formulation of the regular (resp. strongly regular) Hamiltonian system. The notion of the regularization of the second order Lagrangians is presented. The regularization procedure is applied to concrete example.},
author = {Smetanová, Dana},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Hamilton extremals; Dedecker–Hamilton extremals; Hamilton equations; Lagrangian; Lepagean equivalents; Poincaré–Cartan form; regular and strongly regular systems},
language = {eng},
number = {2},
pages = {157-165},
publisher = {Palacký University Olomouc},
title = {The Regularization of the Second Order Lagrangians in Example},
url = {http://eudml.org/doc/287887},
volume = {55},
year = {2016},
}

TY - JOUR
AU - Smetanová, Dana
TI - The Regularization of the Second Order Lagrangians in Example
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2016
PB - Palacký University Olomouc
VL - 55
IS - 2
SP - 157
EP - 165
AB - This paper is devoted to geometric formulation of the regular (resp. strongly regular) Hamiltonian system. The notion of the regularization of the second order Lagrangians is presented. The regularization procedure is applied to concrete example.
LA - eng
KW - Hamilton extremals; Dedecker–Hamilton extremals; Hamilton equations; Lagrangian; Lepagean equivalents; Poincaré–Cartan form; regular and strongly regular systems
UR - http://eudml.org/doc/287887
ER -

References

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  2. Gotay, M. J., A multisymplectic framework for classical field theory and the calculus of variations, I. covariant Hamiltonian formalism, . In: M., Francaviglia, D. D., Holm (eds.): Mechanics, Analysis and Geometry: 200 Years After Lagrange, North-Holland, Amsterdam, 1990, 203–235. (1990) 
  3. Krupka, D., Some geometric aspects of variational problems in fibered manifolds, . Folia Fac. Sci. Nat. 14 (1973), 1–65. (1973) 
  4. Krupka, D., Lepagean forms in higher order variational theory, . In: S., Benenti, M., Francaviglia, A., Lichnerowitz (eds.): Modern Developments in Analytical Mechanics I: Geometrical Dynamics, Proc. IUTAM-ISIM Symp., Accad. delle Scienze di Torino, Torino, 1983, 197–238. (1983) Zbl0572.58003MR0773488
  5. Krupková, O., 10.1016/S0393-0440(01)00087-0, . J. Geom. Phys. 43 (2002), 93–132. (2002) Zbl1016.37033MR1919207DOI10.1016/S0393-0440(01)00087-0
  6. Krupková, O., Hamiltonian field theory revisited: A geometric approach to regularity, . In: Steps in Differential Geometry, Proc. of the Coll. on Diff. Geom., University of Debrecen, Debrecen, 2001, 187–207. (2001) Zbl0980.35009MR1859298
  7. Krupková, O., Smetanová, D., 10.1023/A:1014548309187, . Letters in Math. Phys. 58 (2001), 189–204. (2001) Zbl1005.70025MR1892919DOI10.1023/A:1014548309187
  8. Saunders, D. J., The Geometry of Jets Bundles, . Cambridge University Press, Cambridge, 1989. (1989) MR0989588
  9. Smetanová, D., On regularization of second order Hamiltonian systems, . Arch. Math. 42 (2006), 341–347. (2006) MR2322420
  10. Smetanová, D., On regularization of second order Lagrangians, . In: Global Analysis and Applied Mathematics, American Institut of Physics, Proc. 729, Ankara, 2004, 289–296. (2004) Zbl1119.35328MR2215711
  11. Smetanová, D., The second order lagrangians-regularity problem, . In: 14th Conference on Applied Mathematics, APLIMAT 2015, STU Bratislava, Bratislava, 2015, 690–697. (2015) 

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