LEADER 03726nam  22007095  450 
001 9910717417203321
005 20251216132159.0
010   $a9783031270956$b(electronic bk.)
010   $z9783031270949
024 7 $a10.1007/978-3-031-27095-6
035   $a(MiAaPQ)EBC7241376
035   $a(Au-PeEL)EBL7241376
035   $a(OCoLC)1377817060
035   $a(DE-He213)978-3-031-27095-6
035   $a(PPN)269660720
035   $a(CKB)26523189800041
035   $a(EXLCZ)9926523189800041
100   $a20230425d2023      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aDynamics through First-Order Differential Equations in the Configuration Space /$fby Jaume Llibre, Rafael Ramírez, Valentín Ramírez
205   $a1st ed. 2023.
210  1$aCham :$cSpringer Nature Switzerland :$cImprint: Birkhäuser,$d2023.
215   $a1 online resource (360 pages)
311 08$aPrint version: Llibre, Jaume Dynamics Through First-Order Differential Equations in the Configuration Space Cham : Springer International Publishing AG,c2023 9783031270949 
320   $aIncludes bibliographical references and index.
327   $aChapter. 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.
330   $aThe 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.
606   $aDifferential equations
606   $aDynamics
606   $aGeometry, Differential
606   $aMathematical physics
606   $aDifferential Equations
606   $aDynamical Systems
606   $aDifferential Geometry
606   $aMathematical Physics
606   $aDinàmica$2thub
606   $aEquacions diferencials$2thub
608   $aLlibres electrònics$2thub
615  0$aDifferential equations.
615  0$aDynamics.
615  0$aGeometry, Differential.
615  0$aMathematical physics.
615 14$aDifferential Equations.
615 24$aDynamical Systems.
615 24$aDifferential Geometry.
615 24$aMathematical Physics.
615  7$aDinàmica
615  7$aEquacions diferencials
676   $a620.104
700   $aLlibre$b Jaume$053452
702   $aRami?rez$b Rafael$c(Computer scientist)
702   $aRami?rez$b Valenti?n
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
912   $a9910717417203321
996   $aDynamics through first-order differential equations in the configuration space$93417387
997   $aUNINA