{"text_format":"2","workbook":"xls","n_sheets":1,"sheets":["report2"],"not_rendered":{"charts":0,"images":0,"macros":0,"external_links":1,"defined_names":1,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"run_cost":"one","rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"report2","index":0,"n_rows":27,"n_cols":5,"rows_kept":27,"cut":false,"hidden":false,"merged":[[0,2,0,3],[0,4,0,5],[1,2,1,3],[1,4,1,5],[2,2,2,3],[2,4,2,5],[3,2,3,3],[4,2,4,3],[6,2,6,3],[7,2,7,3],[8,2,8,3],[9,2,9,3],[20,2,20,3],[21,2,21,3],[24,2,24,3]],"flags":["formulas_cached_only"]}
[null,"1.","Record Nr.",null,"UNINA9910717417203321"]
[null,null,"Autore",null,"Llibre Jaume"]
[null,null,"Titolo",null,"Dynamics through First-Order Differential Equations in the Configuration Space / / by Jaume Llibre, Rafael Ramírez, Valentín Ramírez"]
[null,null,"Pubbl/distr/stampa",null,"Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2023"]
[null,null,"ISBN",null,"9783031270956"]
[{"$nulls":4},"9783031270949"]
[null,null,"Edizione",null,"[1st ed. 2023.]"]
[null,null,"Descrizione fisica",null,"1 online resource (360 pages)"]
[null,null,"Disciplina",null,"620.104"]
[null,null,"Soggetti",null,"Differential equations"]
[{"$nulls":4},"Dynamics"]
[{"$nulls":4},"Geometry, Differential"]
[{"$nulls":4},"Mathematical physics"]
[{"$nulls":4},"Differential Equations"]
[{"$nulls":4},"Dynamical Systems"]
[{"$nulls":4},"Differential Geometry"]
[{"$nulls":4},"Mathematical Physics"]
[{"$nulls":4},"Dinàmica"]
[{"$nulls":4},"Equacions diferencials"]
[{"$nulls":4},"Llibres electrònics"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"Chapter. 1. Dynamics via the first order ordinary differential equations -- Chapter. 2. Constrained Cartesian vector fields -- Chapter. 3. Three dimensional constrained Cartesian vector fields -- Chapter. 4. Cartesian-Synge-Cinsov vector field -- Chapter. 5. Generalized Cartesian-Nambu vector fields -- Chapter. 6. Integrability of generalized Cartesian-Nambu vector fields."]
[null,null,null,"Sommario/riassunto","The goal of this monograph is to answer the question, is it possible to solve the dynamics problem inside the configuration space instead of the phase space? By introducing a proper class of vector field – the Cartesian vector field – given in a Riemann space, the authors explore the connections between the first order ordinary differential equations (ODEs) associated to the Cartesian vector field in the configuration space of a given mechanical system and its dynamics. The result is a "]
[{"$nulls":4},"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."]