| Description |
1 online resource (xxii, 345 pages) : illustrations |
| Contents |
Chapter. 1. Dynamics via the first order ordinary differential equations -- Chapter. 2. Constrained Cartesian vector fields -- Chapter. 3. Three dimensional constrained Cartesian vector fields -- Chapter. 4. Cartesian-Synge-Cinsov vector field -- Chapter. 5. Generalized Cartesian-Nambu vector fields -- Chapter. 6. Integrability of generalized Cartesian-Nambu vector fields |
| Summary |
The goal of this monograph is to answer the question, is it possible to solve the dynamics problem inside the configuration space instead of the phase space? By introducing a proper class of vector field the Cartesian vector field given in a Riemann space, the authors explore the connections between the first order ordinary differential equations (ODEs) associated to the Cartesian vector field in the configuration space of a given mechanical system and its dynamics. The result is a new perspective for studying the dynamics of mechanical systems, which allows the authors to present new cases of integrability for the Suslov and Veselova problem; establish the relation between the Cartesian vector field and the integrability of the geodesic flow in a special class of homogeneous surfaces; discuss the importance of the Nambu bracket in the study of first order ODEs; and offer a solution of the inverse problem in celestial mechanics |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Description based on online resource; title from digital title page (viewed on June 05, 2023) |
| Subject |
Dynamics -- Mathematics
|
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Configuration space.
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Differential equations.
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Configuration space
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Differential equations
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Dynamics -- Mathematics
|
| Form |
Electronic book
|
| Author |
Ramírez, Rafael (Computer scientist), author.
|
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Ramírez, Valentín, author
|
| ISBN |
9783031270956 |
|
3031270959 |
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