Dynamics through First-Order Differential Equations in the Configuration Space / / by Jaume Llibre, Rafael Ramírez, Valentín Ramírez

• Record Nr.: UNINA9910717417203321
• Autore: Llibre Jaume
• Pubbl/distr/stampa: Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2023
• ISBN: 9783031270956; 9783031270949
• Edizione: [1st ed. 2023.]
• Descrizione fisica: 1 online resource (360 pages)
• Disciplina: 620.104
• Soggetti: Differential equations; Dynamics; Geometry, Differential; Mathematical physics; Differential Equations; Dynamical Systems; Differential Geometry; Mathematical Physics; Dinàmica; Equacions diferencials; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• 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.