The Geometry of Higher-Order Lagrange Spaces: Applications to Mechanics and Physics: 82 (Fundamental Theories of Physics, 82) - Hardcover
Synopsis
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.
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Synopsis
This monograph is devoted to the problem of the geometrizing of Lagrangians which depend on higher-order accelerations. It presents a construction of the geometry of the total space of the bundle of the accelerations of order k>=1. A geometrical study of the notion of the higher-order Lagrange space is conducted, and the old problem of prolongation of Riemannian spaces to k-osculator manifolds is solved. Also, the geometrical ground for variational calculus on the integral of actions involving higher-order Lagrangians is dealt with. Applications to higher-order analytical mechanics and theoretical physics are included as well. This volume will be of interest to scientists whose work involves differential geometry, mechanics of particles and systems, calculus of variation and optimal control, optimization, optics, electromagnetic theory, and biology.
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The Geometry of Higher-Order Lagrange Spaces: Applications to Mechanics and Physics (Fundamental Theories of Physics, 82)
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The geometry of higher-order Lagrange spaces. Applications to mechanics and physics.
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The Geometry of Higher-Order Lagrange Spaces
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Springer Netherlands Jan 1997, 1997
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 356 pp. Englisch. Seller Inventory # 9780792343936
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The Geometry of Higher-Order Lagrange Spaces
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Gebunden. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Preface. 1. Lagrange Spaces of Order 1. 2. The Geometry of 2-Osculator Bundle. 3. N-Linear Connections. 4. Lagrangians of Second Order. Variational Problem. Noether Type Theorems. 5. Second Order Lagrange Spaces. 6. Geometry of the k-Osculator Bundle. 7. Seller Inventory # 5967993
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The Geometry of Higher-Order Lagrange Spaces | Applications to Mechanics and Physics
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Buch. Condition: Neu. The Geometry of Higher-Order Lagrange Spaces | Applications to Mechanics and Physics | R. Miron | Buch | Fundamental Theories of Physics | xv | Englisch | 1997 | Springer | EAN 9780792343936 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand. Seller Inventory # 102550743
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The Geometry of Higher-Order Lagrange Spaces. Applications to Mechanics and Physics.
Published by
Kluwer Academic Publishers, 1997
ISBN 10: 079234393X
ISBN 13: 9780792343936
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Condition: New. Devoted to the problem of the geometrizing of Lagrangians which depend on higher-order accelerations, this volume presents a construction of the geometry of the total space of the bundle of the accelerations of order k>=1. It is suitable for scientists whose work involves differential geometry and mechanics of particles and systems. Series: Fundamental Theories of Physics. Num Pages: 351 pages, biography. BIC Classification: PBMP; PH. Category: (P) Professional & Vocational. Dimension: 297 x 210 x 20. Weight in Grams: 675. . 1997. Hardback. . . . . Seller Inventory # V9780792343936
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The Geometry of Higher-Order Lagrange Spaces
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Springer, Springer Netherlands Jan 1997, 1997
ISBN 10: 079234393X
ISBN 13: 9780792343936
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Buch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -Preface. 1. Lagrange Spaces of Order 1. 2. The Geometry of 2-Osculator Bundle. 3. N-Linear Connections. 4. Lagrangians of Second Order. Variational Problem. Nöther Type Theorems. 5. Second Order Lagrange Spaces. 6. Geometry of the k-Osculator Bundle. 7. Linear Connections of OsckM. 8. Lagrangians of Order k. Applications to Higher-Order Analytical Mechanics. 9. Prolongation of the Riemannian, Finslerian and Lagrangian Structures to the k-Osculator Bundle. 10. Higher Order Lagrange Spaces. 11. Subspaces in Higher Order Lagrange Spaces. 12. Gauge Theory in the Higher Order Lagrange Spaces. References. Index.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 356 pp. Englisch. Seller Inventory # 9780792343936
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The Geometry of Higher-Order Lagrange Spaces : Applications to Mechanics and Physics
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Seller Inventory # 9780792343936
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The Geometry of Higher-Order Lagrange Spaces. Applications to Mechanics and Physics.
Published by
Kluwer Academic Publishers, 1997
ISBN 10: 079234393X
ISBN 13: 9780792343936
New
Hardcover
Seller: Kennys Bookstore, Olney, MD, U.S.A.
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Condition: New. Devoted to the problem of the geometrizing of Lagrangians which depend on higher-order accelerations, this volume presents a construction of the geometry of the total space of the bundle of the accelerations of order k>=1. It is suitable for scientists whose work involves differential geometry and mechanics of particles and systems. Series: Fundamental Theories of Physics. Num Pages: 351 pages, biography. BIC Classification: PBMP; PH. Category: (P) Professional & Vocational. Dimension: 297 x 210 x 20. Weight in Grams: 675. . 1997. Hardback. . . . . Books ship from the US and Ireland. Seller Inventory # V9780792343936