- Previous Article
- JGM Home
- This Issue
-
Next Article
Stable closed equilibria for anisotropic surface energies: Surfaces with edges
Lagrangian dynamics of submanifolds. Relativistic mechanics
1. | Department of Theoretical Physics, Moscow State University, Moscow, Russian Federation |
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), 301-330.
doi: 10.1142/S0129055X91000114. |
[2] |
G. Giachetta, L. Mangiarotti and G. Sardanashvily, "New Lagrangian and Hamiltonian Methods in Field Theory," World Scientific Publishing Co., Inc., River Edge, NJ, 1997. |
[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), 012903, 19 pp. |
[4] |
G. Giachetta, L. Mangiarotti and G. Sardanashvily, "Advanced Classical Field Theory," World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2009. |
[5] |
G. Giachetta, L. Mangiarotti and G. Sardanashvily, "Geometric Formulation of Classical and Quantum Mechanics," World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2010. |
[6] |
I. Krasil'shchik, V. Lychagin and A. Vinogradov, "Geometry of Jet Spaces and Nonlinear Partial Differential Equations," Gordon and Breach, Glasgow, 1985. |
[7] |
M. De León and P. Rodrigues, "Methods of Differential Geometry in Analytical Mechanics," North-Holland, Amsterdam, 1989. |
[8] |
L. Mangiarotti and G. Sardanashvily, "Gauge Mechanics," World Scientific Publishing Co., Inc., River Edge, NJ, 1998. |
[9] |
M. Modugno and A. Vinogradov, Some variations on the notion of connections, Annali di Matematica Pura ed Applicata, CLXVII (1994), 33-71.
doi: 10.1007/BF01760328. |
[10] |
J. Polchinski, "String Theory," Cambridge University Press, Cambridge, 1998. |
[11] |
G. Sardanashvily, Hamiltonian time-dependent mechanics, Journal of Mathematical Physics, 39 (1998), 2714-2729.
doi: 10.1063/1.532416. |
[12] |
G. Sardanashvily, Relativistic mechanics in a general setting, International Journal of Geometric Methods in Modern Physics, 7 (2010), 1307-1319.
doi: 10.1142/S0219887810004804. |
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), 301-330.
doi: 10.1142/S0129055X91000114. |
[2] |
G. Giachetta, L. Mangiarotti and G. Sardanashvily, "New Lagrangian and Hamiltonian Methods in Field Theory," World Scientific Publishing Co., Inc., River Edge, NJ, 1997. |
[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), 012903, 19 pp. |
[4] |
G. Giachetta, L. Mangiarotti and G. Sardanashvily, "Advanced Classical Field Theory," World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2009. |
[5] |
G. Giachetta, L. Mangiarotti and G. Sardanashvily, "Geometric Formulation of Classical and Quantum Mechanics," World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2010. |
[6] |
I. Krasil'shchik, V. Lychagin and A. Vinogradov, "Geometry of Jet Spaces and Nonlinear Partial Differential Equations," Gordon and Breach, Glasgow, 1985. |
[7] |
M. De León and P. Rodrigues, "Methods of Differential Geometry in Analytical Mechanics," North-Holland, Amsterdam, 1989. |
[8] |
L. Mangiarotti and G. Sardanashvily, "Gauge Mechanics," World Scientific Publishing Co., Inc., River Edge, NJ, 1998. |
[9] |
M. Modugno and A. Vinogradov, Some variations on the notion of connections, Annali di Matematica Pura ed Applicata, CLXVII (1994), 33-71.
doi: 10.1007/BF01760328. |
[10] |
J. Polchinski, "String Theory," Cambridge University Press, Cambridge, 1998. |
[11] |
G. Sardanashvily, Hamiltonian time-dependent mechanics, Journal of Mathematical Physics, 39 (1998), 2714-2729.
doi: 10.1063/1.532416. |
[12] |
G. Sardanashvily, Relativistic mechanics in a general setting, International Journal of Geometric Methods in Modern Physics, 7 (2010), 1307-1319.
doi: 10.1142/S0219887810004804. |
[1] |
Melvin Leok, Diana Sosa. Dirac structures and Hamilton-Jacobi theory for Lagrangian mechanics on Lie algebroids. Journal of Geometric Mechanics, 2012, 4 (4) : 421-442. doi: 10.3934/jgm.2012.4.421 |
[2] |
Robert M. Strain. Coordinates in the relativistic Boltzmann theory. Kinetic and Related Models, 2011, 4 (1) : 345-359. doi: 10.3934/krm.2011.4.345 |
[3] |
Henry O. Jacobs, Hiroaki Yoshimura. Tensor products of Dirac structures and interconnection in Lagrangian mechanics. Journal of Geometric Mechanics, 2014, 6 (1) : 67-98. doi: 10.3934/jgm.2014.6.67 |
[4] |
Juan Carlos Marrero, David Martín de Diego, Ari Stern. Symplectic groupoids and discrete constrained Lagrangian mechanics. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 367-397. doi: 10.3934/dcds.2015.35.367 |
[5] |
Rémi Leclercq. Spectral invariants in Lagrangian Floer theory. Journal of Modern Dynamics, 2008, 2 (2) : 249-286. doi: 10.3934/jmd.2008.2.249 |
[6] |
Eduard Feireisl, Šárka Nečasová, Reimund Rautmann, Werner Varnhorn. New developments in mathematical theory of fluid mechanics. Discrete and Continuous Dynamical Systems - S, 2014, 7 (5) : i-ii. doi: 10.3934/dcdss.2014.7.5i |
[7] |
José Antonio Alcántara, Simone Calogero. On a relativistic Fokker-Planck equation in kinetic theory. Kinetic and Related Models, 2011, 4 (2) : 401-426. doi: 10.3934/krm.2011.4.401 |
[8] |
Benjamin Seibold, Rodolfo R. Rosales, Jean-Christophe Nave. Jet schemes for advection problems. Discrete and Continuous Dynamical Systems - B, 2012, 17 (4) : 1229-1259. doi: 10.3934/dcdsb.2012.17.1229 |
[9] |
Katarzyna Grabowska. Lagrangian and Hamiltonian formalism in Field Theory: A simple model. Journal of Geometric Mechanics, 2010, 2 (4) : 375-395. doi: 10.3934/jgm.2010.2.375 |
[10] |
Giuseppe Marmo, Giuseppe Morandi, Narasimhaiengar Mukunda. The Hamilton-Jacobi theory and the analogy between classical and quantum mechanics. Journal of Geometric Mechanics, 2009, 1 (3) : 317-355. doi: 10.3934/jgm.2009.1.317 |
[11] |
Weinan E, Jianfeng Lu. Mathematical theory of solids: From quantum mechanics to continuum models. Discrete and Continuous Dynamical Systems, 2014, 34 (12) : 5085-5097. doi: 10.3934/dcds.2014.34.5085 |
[12] |
Jean-Marie Souriau. On Geometric Mechanics. Discrete and Continuous Dynamical Systems, 2007, 19 (3) : 595-607. doi: 10.3934/dcds.2007.19.595 |
[13] |
E. Camouzis, H. Kollias, I. Leventides. Stable manifold market sequences. Journal of Dynamics and Games, 2018, 5 (2) : 165-185. doi: 10.3934/jdg.2018010 |
[14] |
Camillo De Lellis, Emanuele Spadaro. Center manifold: A case study. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1249-1272. doi: 10.3934/dcds.2011.31.1249 |
[15] |
Zhiguo Feng, Ka-Fai Cedric Yiu. Manifold relaxations for integer programming. Journal of Industrial and Management Optimization, 2014, 10 (2) : 557-566. doi: 10.3934/jimo.2014.10.557 |
[16] |
Robert I. McLachlan, Ander Murua. The Lie algebra of classical mechanics. Journal of Computational Dynamics, 2019, 6 (2) : 345-360. doi: 10.3934/jcd.2019017 |
[17] |
Gianne Derks. Book review: Geometric mechanics. Journal of Geometric Mechanics, 2009, 1 (2) : 267-270. doi: 10.3934/jgm.2009.1.267 |
[18] |
Andrew D. Lewis. The physical foundations of geometric mechanics. Journal of Geometric Mechanics, 2017, 9 (4) : 487-574. doi: 10.3934/jgm.2017019 |
[19] |
Andrew D. Lewis. Nonholonomic and constrained variational mechanics. Journal of Geometric Mechanics, 2020, 12 (2) : 165-308. doi: 10.3934/jgm.2020013 |
[20] |
Jean-Claude Zambrini. Stochastic deformation of classical mechanics. Conference Publications, 2013, 2013 (special) : 807-813. doi: 10.3934/proc.2013.2013.807 |
2020 Impact Factor: 0.857
Tools
Metrics
Other articles
by authors
[Back to Top]