Lagrangian dynamics of submanifolds. Relativistic mechanics

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March 2012, 4(1): 99-110. doi: 10.3934/jgm.2012.4.99

Lagrangian dynamics of submanifolds. Relativistic mechanics

1.	Department of Theoretical Physics, Moscow State University, Moscow, Russian Federation

Received September 2011 Revised January 2012 Published April 2012

Abstract
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Geometric formulation of Lagrangian relativistic mechanics in the terms of jets of one-dimensional submanifolds is generalized to Lagrangian theory of submanifolds of arbitrary dimension.

Keywords: Lagrangian theory, jet manifold, relativistic mechanics..

Mathematics Subject Classification: Primary: 58A20, 70H40; Secondary: 83A0.

Citation: Gennadi Sardanashvily. Lagrangian dynamics of submanifolds. Relativistic mechanics. Journal of Geometric Mechanics, 2012, 4 (1) : 99-110. doi: 10.3934/jgm.2012.4.99

References:

[1]	A. Echeverría Enríquez, M. Muñoz Lecanda and N. Román Roy, Geometrical setting of time-dependent regular systems. Alternative models,, Reviews in Mathematical Physica, 3 (1991), 301. doi: 10.1142/S0129055X91000114. Google Scholar
[2]	G. Giachetta, L. Mangiarotti and G. Sardanashvily, "New Lagrangian and Hamiltonian Methods in Field Theory,", World Scientific Publishing Co., (1997). Google Scholar
[3]	G. Giachetta, L. Mangiarotti and G. Sardanashvily, On the notion of gauge symmetries of generic Lagrangian field theory,, Journal of Mathematical Physics, 50 (2009). Google Scholar
[4]	G. Giachetta, L. Mangiarotti and G. Sardanashvily, "Advanced Classical Field Theory,", World Scientific Publishing Co. Pte. Ltd., (2009). Google Scholar
[5]	G. Giachetta, L. Mangiarotti and G. Sardanashvily, "Geometric Formulation of Classical and Quantum Mechanics,", World Scientific Publishing Co. Pte. Ltd., (2010). Google Scholar
[6]	I. Krasil'shchik, V. Lychagin and A. Vinogradov, "Geometry of Jet Spaces and Nonlinear Partial Differential Equations,", Gordon and Breach, (1985). Google Scholar
[7]	M. De León and P. Rodrigues, "Methods of Differential Geometry in Analytical Mechanics,", North-Holland, (1989). Google Scholar
[8]	L. Mangiarotti and G. Sardanashvily, "Gauge Mechanics,", World Scientific Publishing Co., (1998). Google Scholar
[9]	M. Modugno and A. Vinogradov, Some variations on the notion of connections,, Annali di Matematica Pura ed Applicata, CLXVII (1994), 33. doi: 10.1007/BF01760328. Google Scholar
[10]	J. Polchinski, "String Theory,", Cambridge University Press, (1998). Google Scholar
[11]	G. Sardanashvily, Hamiltonian time-dependent mechanics,, Journal of Mathematical Physics, 39 (1998), 2714. doi: 10.1063/1.532416. Google Scholar
[12]	G. Sardanashvily, Relativistic mechanics in a general setting,, International Journal of Geometric Methods in Modern Physics, 7 (2010), 1307. doi: 10.1142/S0219887810004804. Google Scholar

show all references

References:

[1]	A. Echeverría Enríquez, M. Muñoz Lecanda and N. Román Roy, Geometrical setting of time-dependent regular systems. Alternative models,, Reviews in Mathematical Physica, 3 (1991), 301. doi: 10.1142/S0129055X91000114. Google Scholar
[2]	G. Giachetta, L. Mangiarotti and G. Sardanashvily, "New Lagrangian and Hamiltonian Methods in Field Theory,", World Scientific Publishing Co., (1997). Google Scholar
[3]	G. Giachetta, L. Mangiarotti and G. Sardanashvily, On the notion of gauge symmetries of generic Lagrangian field theory,, Journal of Mathematical Physics, 50 (2009). Google Scholar
[4]	G. Giachetta, L. Mangiarotti and G. Sardanashvily, "Advanced Classical Field Theory,", World Scientific Publishing Co. Pte. Ltd., (2009). Google Scholar
[5]	G. Giachetta, L. Mangiarotti and G. Sardanashvily, "Geometric Formulation of Classical and Quantum Mechanics,", World Scientific Publishing Co. Pte. Ltd., (2010). Google Scholar
[6]	I. Krasil'shchik, V. Lychagin and A. Vinogradov, "Geometry of Jet Spaces and Nonlinear Partial Differential Equations,", Gordon and Breach, (1985). Google Scholar
[7]	M. De León and P. Rodrigues, "Methods of Differential Geometry in Analytical Mechanics,", North-Holland, (1989). Google Scholar
[8]	L. Mangiarotti and G. Sardanashvily, "Gauge Mechanics,", World Scientific Publishing Co., (1998). Google Scholar
[9]	M. Modugno and A. Vinogradov, Some variations on the notion of connections,, Annali di Matematica Pura ed Applicata, CLXVII (1994), 33. doi: 10.1007/BF01760328. Google Scholar
[10]	J. Polchinski, "String Theory,", Cambridge University Press, (1998). Google Scholar
[11]	G. Sardanashvily, Hamiltonian time-dependent mechanics,, Journal of Mathematical Physics, 39 (1998), 2714. doi: 10.1063/1.532416. Google Scholar
[12]	G. Sardanashvily, Relativistic mechanics in a general setting,, International Journal of Geometric Methods in Modern Physics, 7 (2010), 1307. doi: 10.1142/S0219887810004804. Google Scholar

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