The Geometry of Higher-Order Lagrange Spaces: Applications to Mechanics and Physics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1997
|
| Schriftenreihe: | Fundamental Theories of Physics, An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application
82 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This monograph is mostly devoted to the problem of the geome trizing of Lagrangians which depend on higher order accelerations. It naturally prolongs the theme of the monograph "The Geometry of La grange spaces: Theory and Applications", written together with M. Anastasiei and published by Kluwer Academic Publishers in 1994. The existence of Lagrangians of order k > 1 has been contemplated by mechanicists and physicists for a long time. Einstein had grasped their presence in connection with the Brownian motion. They are also present in relativistic theories based on metrics which depend on speeds and accelerations of particles or in the Hamiltonian formulation of non linear systems given by Korteweg-de Vries equations. There resulted from here the methods to be adopted in their theoretical treatment. One is based on the variational problem involving the integral action of the Lagrangian. A second one is derived from the axioms of Analytical Mechanics involving the Poincare-Cartan forms. The geometrical methods based on the study of the geometries of higher order could invigorate the whole theory. This is the way adopted by us in defining and studying the Lagrange spaces of higher order. The problems raised by the geometrization of Lagrangians of order k > 1 investigated by many scholars: Ch. Ehresmann, P. Libermann, J. Pommaret; J.T. Synge, M. Crampin, P. Saunders; G.S. Asanov, P.Aringazin; I. Kolar, D. Krupka; M. de Leon, W. Sarlet, P. Cantrjin, H. Rund, W.M. Tulczyjew, A. Kawaguchi, K. Yano, K. Kondo, D. |
| Beschreibung: | 1 Online-Ressource (XV, 336 p) |
| ISBN: | 9789401733380 9789048147892 |
| DOI: | 10.1007/978-94-017-3338-0 |
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| spelling | Miron, Radu Verfasser aut The Geometry of Higher-Order Lagrange Spaces Applications to Mechanics and Physics by Radu Miron Dordrecht Springer Netherlands 1997 1 Online-Ressource (XV, 336 p) txt rdacontent c rdamedia cr rdacarrier Fundamental Theories of Physics, An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application 82 This monograph is mostly devoted to the problem of the geome trizing of Lagrangians which depend on higher order accelerations. It naturally prolongs the theme of the monograph "The Geometry of La grange spaces: Theory and Applications", written together with M. Anastasiei and published by Kluwer Academic Publishers in 1994. The existence of Lagrangians of order k > 1 has been contemplated by mechanicists and physicists for a long time. Einstein had grasped their presence in connection with the Brownian motion. They are also present in relativistic theories based on metrics which depend on speeds and accelerations of particles or in the Hamiltonian formulation of non linear systems given by Korteweg-de Vries equations. There resulted from here the methods to be adopted in their theoretical treatment. One is based on the variational problem involving the integral action of the Lagrangian. A second one is derived from the axioms of Analytical Mechanics involving the Poincare-Cartan forms. The geometrical methods based on the study of the geometries of higher order could invigorate the whole theory. This is the way adopted by us in defining and studying the Lagrange spaces of higher order. The problems raised by the geometrization of Lagrangians of order k > 1 investigated by many scholars: Ch. Ehresmann, P. Libermann, J. Pommaret; J.T. Synge, M. Crampin, P. Saunders; G.S. Asanov, P.Aringazin; I. Kolar, D. Krupka; M. de Leon, W. Sarlet, P. Cantrjin, H. Rund, W.M. Tulczyjew, A. Kawaguchi, K. Yano, K. Kondo, D. Mathematics Global differential geometry Mathematical optimization Mechanics Differential Geometry Theoretical, Mathematical and Computational Physics Calculus of Variations and Optimal Control; Optimization Optics, Optoelectronics, Plasmonics and Optical Devices Mathematik Ordnung n (DE-588)4322729-6 gnd rswk-swf Lagrange-Raum (DE-588)4458304-7 gnd rswk-swf Lagrange-Raum (DE-588)4458304-7 s Ordnung n (DE-588)4322729-6 s 1\p DE-604 https://doi.org/10.1007/978-94-017-3338-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Miron, Radu The Geometry of Higher-Order Lagrange Spaces Applications to Mechanics and Physics Mathematics Global differential geometry Mathematical optimization Mechanics Differential Geometry Theoretical, Mathematical and Computational Physics Calculus of Variations and Optimal Control; Optimization Optics, Optoelectronics, Plasmonics and Optical Devices Mathematik Ordnung n (DE-588)4322729-6 gnd Lagrange-Raum (DE-588)4458304-7 gnd |
| subject_GND | (DE-588)4322729-6 (DE-588)4458304-7 |
| title | The Geometry of Higher-Order Lagrange Spaces Applications to Mechanics and Physics |
| title_auth | The Geometry of Higher-Order Lagrange Spaces Applications to Mechanics and Physics |
| title_exact_search | The Geometry of Higher-Order Lagrange Spaces Applications to Mechanics and Physics |
| title_full | The Geometry of Higher-Order Lagrange Spaces Applications to Mechanics and Physics by Radu Miron |
| title_fullStr | The Geometry of Higher-Order Lagrange Spaces Applications to Mechanics and Physics by Radu Miron |
| title_full_unstemmed | The Geometry of Higher-Order Lagrange Spaces Applications to Mechanics and Physics by Radu Miron |
| title_short | The Geometry of Higher-Order Lagrange Spaces |
| title_sort | the geometry of higher order lagrange spaces applications to mechanics and physics |
| title_sub | Applications to Mechanics and Physics |
| topic | Mathematics Global differential geometry Mathematical optimization Mechanics Differential Geometry Theoretical, Mathematical and Computational Physics Calculus of Variations and Optimal Control; Optimization Optics, Optoelectronics, Plasmonics and Optical Devices Mathematik Ordnung n (DE-588)4322729-6 gnd Lagrange-Raum (DE-588)4458304-7 gnd |
| topic_facet | Mathematics Global differential geometry Mathematical optimization Mechanics Differential Geometry Theoretical, Mathematical and Computational Physics Calculus of Variations and Optimal Control; Optimization Optics, Optoelectronics, Plasmonics and Optical Devices Mathematik Ordnung n Lagrange-Raum |
| url | https://doi.org/10.1007/978-94-017-3338-0 |
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