Dynamical Systems and Geometric Mechanics: an Introduction
Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin
De Gruyter
[2018]
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| Ausgabe: | 2nd edition |
| Schriftenreihe: | De Gruyter Studies in Mathematical Physics
48 |
| Schlagworte: | |
| Online-Zugang: | DE-634 DE-M347 DE-859 DE-860 DE-739 DE-1046 DE-1043 DE-858 Volltext Inhaltsverzeichnis |
| Zusammenfassung: | Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincaré maps, Floquet theory, the Poincaré-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms |
| Beschreibung: | 1 Online-Ressource (XII, 336 Seiten) Illustrationen, Diagramme |
| ISBN: | 9783110597806 9783110598032 |
| DOI: | 10.1515/9783110597806 |
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| 505 | 8 | |a Frontmatter -- - Contents -- - Preface - Maruskin, Jared M. -- - Part I: Dynamical Systems -- - 1. Linear Systems -- - 2. Linearization Of Trajectories -- - 3. Invariant Manifolds -- - 4. Periodic Orbits -- - 5. Bifurcations And Chaos -- - Part II: Geometric Mechanics -- - 6. Differentiable Manifolds -- - 7. Lagrangian Mechanics -- - 8. Hamiltonian Mechanics -- - 9. Lie Groups And Rigid-Body Mechanics -- - 10. Moving Frames And Nonholonomic Mechanics -- - 11. Fiber Bundles And Nonholonomic Mechanics -- - Bibliography -- - Index. - Mode of access: Internet via World Wide Web | |
| 520 | |a Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincaré maps, Floquet theory, the Poincaré-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms | ||
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| contents | Frontmatter -- - Contents -- - Preface - Maruskin, Jared M. -- - Part I: Dynamical Systems -- - 1. Linear Systems -- - 2. Linearization Of Trajectories -- - 3. Invariant Manifolds -- - 4. Periodic Orbits -- - 5. Bifurcations And Chaos -- - Part II: Geometric Mechanics -- - 6. Differentiable Manifolds -- - 7. Lagrangian Mechanics -- - 8. Hamiltonian Mechanics -- - 9. Lie Groups And Rigid-Body Mechanics -- - 10. Moving Frames And Nonholonomic Mechanics -- - 11. Fiber Bundles And Nonholonomic Mechanics -- - Bibliography -- - Index. - Mode of access: Internet via World Wide Web |
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| dewey-full | 515/.39 |
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| discipline | Physik Mathematik |
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| indexdate | 2025-02-19T17:24:31Z |
| institution | BVB |
| isbn | 9783110597806 9783110598032 |
| language | English |
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| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | De Gruyter |
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| series | De Gruyter Studies in Mathematical Physics |
| series2 | De Gruyter Studies in Mathematical Physics |
| spelling | Maruskin, Jared M. Verfasser (DE-588)102699988X aut Dynamical Systems and Geometric Mechanics an Introduction Jared Michael Maruskin 2nd edition Berlin De Gruyter [2018] © 2018 1 Online-Ressource (XII, 336 Seiten) Illustrationen, Diagramme txt rdacontent c rdamedia cr rdacarrier De Gruyter Studies in Mathematical Physics 48 Frontmatter -- - Contents -- - Preface - Maruskin, Jared M. -- - Part I: Dynamical Systems -- - 1. Linear Systems -- - 2. Linearization Of Trajectories -- - 3. Invariant Manifolds -- - 4. Periodic Orbits -- - 5. Bifurcations And Chaos -- - Part II: Geometric Mechanics -- - 6. Differentiable Manifolds -- - 7. Lagrangian Mechanics -- - 8. Hamiltonian Mechanics -- - 9. Lie Groups And Rigid-Body Mechanics -- - 10. Moving Frames And Nonholonomic Mechanics -- - 11. Fiber Bundles And Nonholonomic Mechanics -- - Bibliography -- - Index. - Mode of access: Internet via World Wide Web Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincaré maps, Floquet theory, the Poincaré-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms In English Differentiable dynamical systems Geometry, Differential Mechanics, Analytic Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Theoretische Mechanik (DE-588)4185100-6 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Differentialgeometrie (DE-588)4012248-7 s Theoretische Mechanik (DE-588)4185100-6 s DE-604 Erscheint auch als Druck-Ausgabe 9783110598032 Erscheint auch als Druck-Ausgabe 9783110597295 De Gruyter Studies in Mathematical Physics 48 (DE-604)BV042029665 48 https://doi.org/10.1515/9783110597806 Verlag URL des Erstveröffentlichers Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030552710&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Maruskin, Jared M. Dynamical Systems and Geometric Mechanics an Introduction De Gruyter Studies in Mathematical Physics Frontmatter -- - Contents -- - Preface - Maruskin, Jared M. -- - Part I: Dynamical Systems -- - 1. Linear Systems -- - 2. Linearization Of Trajectories -- - 3. Invariant Manifolds -- - 4. Periodic Orbits -- - 5. Bifurcations And Chaos -- - Part II: Geometric Mechanics -- - 6. Differentiable Manifolds -- - 7. Lagrangian Mechanics -- - 8. Hamiltonian Mechanics -- - 9. Lie Groups And Rigid-Body Mechanics -- - 10. Moving Frames And Nonholonomic Mechanics -- - 11. Fiber Bundles And Nonholonomic Mechanics -- - Bibliography -- - Index. - Mode of access: Internet via World Wide Web Differentiable dynamical systems Geometry, Differential Mechanics, Analytic Differentialgeometrie (DE-588)4012248-7 gnd Dynamisches System (DE-588)4013396-5 gnd Theoretische Mechanik (DE-588)4185100-6 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4013396-5 (DE-588)4185100-6 |
| title | Dynamical Systems and Geometric Mechanics an Introduction |
| title_auth | Dynamical Systems and Geometric Mechanics an Introduction |
| title_exact_search | Dynamical Systems and Geometric Mechanics an Introduction |
| title_full | Dynamical Systems and Geometric Mechanics an Introduction Jared Michael Maruskin |
| title_fullStr | Dynamical Systems and Geometric Mechanics an Introduction Jared Michael Maruskin |
| title_full_unstemmed | Dynamical Systems and Geometric Mechanics an Introduction Jared Michael Maruskin |
| title_short | Dynamical Systems and Geometric Mechanics |
| title_sort | dynamical systems and geometric mechanics an introduction |
| title_sub | an Introduction |
| topic | Differentiable dynamical systems Geometry, Differential Mechanics, Analytic Differentialgeometrie (DE-588)4012248-7 gnd Dynamisches System (DE-588)4013396-5 gnd Theoretische Mechanik (DE-588)4185100-6 gnd |
| topic_facet | Differentiable dynamical systems Geometry, Differential Mechanics, Analytic Differentialgeometrie Dynamisches System Theoretische Mechanik |
| url | https://doi.org/10.1515/9783110597806 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030552710&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV042029665 |
| work_keys_str_mv | AT maruskinjaredm dynamicalsystemsandgeometricmechanicsanintroduction |