Dynamics Through First-order Differential Equations in the Configuration Space - Rilegato

Llibre, Jaume; Ramrez, Rafael; Ramrez, Valentn

 
9783031270949: Dynamics Through First-order Differential Equations in the Configuration Space
Rilegato
ISBN 10: 3031270940 ISBN 13: 9783031270949
Casa editrice: Birkhauser, 2023

Sinossi

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.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Informazioni sull?autore

Jaume Llibre is full professor at the Autonomous University of Barcelona (Spain) and a member of the Royal Academy of Sciences and Arts of Barcelona. He was a long-term visitor at different universities and research institutes. He is the author of many papers and has a large number of collaborators and Ph.D. students. His main results deal with periodic orbits, integrability, averaging theory, polynomial vector fields, Hamiltonian systems, celestial mechanics, and topological entropy.

Rafael Ramírez studied at the Peoples Friendship University (UDN) and read his PhD thesis under the direction of Professor A.C. Galiullin. He is a professor at the Rovira i Virgili University of Tarragona (Spain) and is a collaborator of PhD students. His main results deal with the inverse problem of ordinary differential equations, mechanics, and nonholonomic systems.

Valentín Ramírez studied at the University of Barcelona and read his PhD thesis under the direction of Professor J. Llibre. His main results deal with qualitative theory of ordinary differential equations, in particular with the center-focus problem, integrability, and development of mathematical models of financial risks.

Dalla quarta di copertina

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.

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

Editore
Birkhauser
Data di pubblicazione
2023
Lingua
Inglese
ISBN 10 
3031270940
ISBN 13 
9783031270949
Rilegatura
Copertina rigida
Numero di pagine
368
Contatto del produttore
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Altre edizioni note dello stesso titolo

9783031270970: Dynamics through First-Order Differential Equations in the Configuration Space

Edizione in evidenza

ISBN 10:  3031270975 ISBN 13:  9783031270970
Casa editrice: Birkhäuser, 2024
Brossura