Foundations of Theoretical Mechanics II: Birkhoffian Generalizations of Hamiltonian Mechanics
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1983
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| Schriftenreihe: | Texts and Monographs in Physics
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In the preceding volume,l I identified necessary and sufficient conditions for the existence of a representation of given Newtonian systems via a variational principle, the so-called conditions of variational self-adjointness. A primary objective of this volume is to establish that all Newtonian systems satisfying certain locality, regularity, and smoothness conditions, whether conservative or nonconservative, can be treated via conventional variational principles, Lie algebra techniques, and symplectic geometrical formulations. This volume therefore resolves a controversy on the repre sentational capabilities of conventional variational principles that has been 2 lingering in the literature for over a century, as reported in Chart 1. 3. 1. The primary results of this volume are the following. In Chapter 4,3 I prove a Theorem of Direct Universality of the Inverse Problem. It establishes the existence, via a variational principle, of a representation for all Newtonian systems of the class admitted (universality) in the coordinates and time variables of the experimenter (direct universality). The underlying analytic equations turn out to be a generalization of conventional Hamilton equations (those without external terms) which: (a) admit the most general possible action functional for first-order systems; (b) possess a Lie algebra structure in the most general possible, regular realization of the product; and (c) 1 Santilli (1978a). As was the case for Volume I, the references are listed at the end of this volume, first in chronological order and then in alphabetic order |
| Beschreibung: | 1 Online-Ressource (XX, 372 p) |
| ISBN: | 9783642867606 9783642867620 |
| ISSN: | 1864-5879 |
| DOI: | 10.1007/978-3-642-86760-6 |
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Datensatz im Suchindex
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| doi_str_mv | 10.1007/978-3-642-86760-6 |
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| institution | BVB |
| isbn | 9783642867606 9783642867620 |
| issn | 1864-5879 |
| language | English |
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| spelling | Santilli, Ruggero Maria Verfasser aut Foundations of Theoretical Mechanics II Birkhoffian Generalizations of Hamiltonian Mechanics by Ruggero Maria Santilli Berlin, Heidelberg Springer Berlin Heidelberg 1983 1 Online-Ressource (XX, 372 p) txt rdacontent c rdamedia cr rdacarrier Texts and Monographs in Physics 1864-5879 In the preceding volume,l I identified necessary and sufficient conditions for the existence of a representation of given Newtonian systems via a variational principle, the so-called conditions of variational self-adjointness. A primary objective of this volume is to establish that all Newtonian systems satisfying certain locality, regularity, and smoothness conditions, whether conservative or nonconservative, can be treated via conventional variational principles, Lie algebra techniques, and symplectic geometrical formulations. This volume therefore resolves a controversy on the repre sentational capabilities of conventional variational principles that has been 2 lingering in the literature for over a century, as reported in Chart 1. 3. 1. The primary results of this volume are the following. In Chapter 4,3 I prove a Theorem of Direct Universality of the Inverse Problem. It establishes the existence, via a variational principle, of a representation for all Newtonian systems of the class admitted (universality) in the coordinates and time variables of the experimenter (direct universality). The underlying analytic equations turn out to be a generalization of conventional Hamilton equations (those without external terms) which: (a) admit the most general possible action functional for first-order systems; (b) possess a Lie algebra structure in the most general possible, regular realization of the product; and (c) 1 Santilli (1978a). As was the case for Volume I, the references are listed at the end of this volume, first in chronological order and then in alphabetic order Physics Quantum theory Quantum Physics Quantum Information Technology, Spintronics Quantentheorie https://doi.org/10.1007/978-3-642-86760-6 Verlag Volltext |
| spellingShingle | Santilli, Ruggero Maria Foundations of Theoretical Mechanics II Birkhoffian Generalizations of Hamiltonian Mechanics Physics Quantum theory Quantum Physics Quantum Information Technology, Spintronics Quantentheorie |
| title | Foundations of Theoretical Mechanics II Birkhoffian Generalizations of Hamiltonian Mechanics |
| title_auth | Foundations of Theoretical Mechanics II Birkhoffian Generalizations of Hamiltonian Mechanics |
| title_exact_search | Foundations of Theoretical Mechanics II Birkhoffian Generalizations of Hamiltonian Mechanics |
| title_full | Foundations of Theoretical Mechanics II Birkhoffian Generalizations of Hamiltonian Mechanics by Ruggero Maria Santilli |
| title_fullStr | Foundations of Theoretical Mechanics II Birkhoffian Generalizations of Hamiltonian Mechanics by Ruggero Maria Santilli |
| title_full_unstemmed | Foundations of Theoretical Mechanics II Birkhoffian Generalizations of Hamiltonian Mechanics by Ruggero Maria Santilli |
| title_short | Foundations of Theoretical Mechanics II |
| title_sort | foundations of theoretical mechanics ii birkhoffian generalizations of hamiltonian mechanics |
| title_sub | Birkhoffian Generalizations of Hamiltonian Mechanics |
| topic | Physics Quantum theory Quantum Physics Quantum Information Technology, Spintronics Quantentheorie |
| topic_facet | Physics Quantum theory Quantum Physics Quantum Information Technology, Spintronics Quantentheorie |
| url | https://doi.org/10.1007/978-3-642-86760-6 |
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