Dynamics through First-Order Differential Equations in the Configuration Space / / by Jaume Llibre, Rafael Ramírez, Valentín Ramírez
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| Autore: |
Llibre Jaume
|
| Titolo: |
Dynamics through First-Order Differential Equations in the Configuration Space / / by Jaume Llibre, Rafael Ramírez, Valentín Ramírez
|
| Pubblicazione: | Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2023 |
| Edizione: | 1st ed. 2023. |
| Descrizione fisica: | 1 online resource (360 pages) |
| Disciplina: | 620.104 |
| Soggetto topico: | Differential equations |
| Dynamics | |
| Geometry, Differential | |
| Mathematical physics | |
| Differential Equations | |
| Dynamical Systems | |
| Differential Geometry | |
| Mathematical Physics | |
| Dinàmica | |
| Equacions diferencials | |
| Soggetto genere / forma: | Llibres electrònics |
| Persona (resp. second.): | RamírezRafael (Computer scientist) |
| RamírezValentín | |
| Nota di bibliografia: | Includes bibliographical references and index. |
| Nota di contenuto: | 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. |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | Dynamics through first-order differential equations in the configuration space |
| ISBN: | 9783031270956 |
| 9783031270949 | |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910717417203321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |