03726nam 22007095 450 991071741720332120251216132159.09783031270956(electronic bk.)978303127094910.1007/978-3-031-27095-6(MiAaPQ)EBC7241376(Au-PeEL)EBL7241376(OCoLC)1377817060(DE-He213)978-3-031-27095-6(PPN)269660720(CKB)26523189800041(EXLCZ)992652318980004120230425d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierDynamics through First-Order Differential Equations in the Configuration Space /by Jaume Llibre, Rafael Ramírez, Valentín Ramírez1st ed. 2023.Cham :Springer Nature Switzerland :Imprint: Birkhäuser,2023.1 online resource (360 pages)Print version: Llibre, Jaume Dynamics Through First-Order Differential Equations in the Configuration Space Cham : Springer International Publishing AG,c2023 9783031270949 Includes bibliographical references and index.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.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.Differential equationsDynamicsGeometry, DifferentialMathematical physicsDifferential EquationsDynamical SystemsDifferential GeometryMathematical PhysicsDinàmicathubEquacions diferencialsthubLlibres electrònicsthubDifferential equations.Dynamics.Geometry, Differential.Mathematical physics.Differential Equations.Dynamical Systems.Differential Geometry.Mathematical Physics.DinàmicaEquacions diferencials620.104Llibre Jaume53452Ramírez Rafael(Computer scientist)Ramírez ValentínMiAaPQMiAaPQMiAaPQ9910717417203321Dynamics through first-order differential equations in the configuration space3417387UNINA