Free Delivery Over $100
|
|
|||
|
||||
OverviewThe 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. Full Product DetailsAuthor: Jaume Llibre , Rafael Ramírez , Valentín RamírezPublisher: Birkhauser Verlag AG Imprint: Birkhauser Verlag AG Edition: 1st ed. 2023 Weight: 0.717kg ISBN: 9783031270949ISBN 10: 3031270940 Pages: 345 Publication Date: 26 April 2023 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsChapter. 1. Dynamics via the first order ordinary differential equationsChapter. 2. Constrained Cartesian vector fieldsChapter. 3. Three dimensional constrained Cartesian vector fieldsChapter. 4. Cartesian-Synge-Cinsov vector fieldChapter. 5. Generalized Cartesian-Nambu vector fieldsChapter. 6. Integrability of generalized Cartesian-Nambu vector fieldsReviewsAuthor InformationJaume 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. Tab Content 6Author Website:Countries AvailableAll regions |
||||
