Dynamics through First-Order Differential Equations in the Configuration Space - Brossura

Llibre, Jaume; Ramírez, Rafael; Ramírez, Valentín

Brossura

ISBN 10: 3031270967 ISBN 13: 9783031270963

Casa editrice: Birkhäuser, 2023

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.

Dettagli dell'edizione

• Editore: Birkhäuser
• Data di pubblicazione: 2023
• Lingua: Inglese
• ISBN 10: 3031270967
• ISBN 13: 9783031270963
• Rilegatura: Copertina flessibile
• Numero di pagine: 368
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile