Dynamics through First-Order Differential Equations in the Configuration Space

Llibre, Jaume; Ramírez, Rafael; Ramírez, Valentín

ISBN 10: 3031270967 / ISBN 13: 9783031270963

Editore: Birkhäuser, 2023

In. Codice articolo ria9783031270963_new

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.

Dati bibliografici

Titolo: Dynamics through First-Order Differential ...
Casa editrice: Birkhäuser
Data di pubblicazione: 2023
Legatura: Brossura
Condizione: New