000 03269nam a22004935i 4500
001 978-3-319-26339-7
003 DE-He213
005 20181204134227.0
007 cr nn 008mamaa
008 160309s2016 gw | s |||| 0|eng d
020 _a9783319263397
_9978-3-319-26339-7
024 7 _a10.1007/978-3-319-26339-7
_2doi
040 _aISI Library, Kolkata
050 4 _aQA372
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
072 7 _aPBKJ
_2thema
082 0 4 _a515.352
_223
100 1 _aLlibre, Jaume.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aInverse Problems in Ordinary Differential Equations and Applications
_h[electronic resource] /
_cby Jaume Llibre, Rafael Ramírez.
250 _a1st ed. 2016.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Birkhäuser,
_c2016.
300 _aXII, 266 p. 9 illus., 8 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Mathematics,
_x0743-1643 ;
_v313
505 0 _aPreface -- 1.Differential Equations with Given Partial and First Integrals -- 2.Polynomial Vector Fields with Given Partial and First Integrals -- 3.16th Hilbert Problem for Algebraic Limit Cycles -- 4.Inverse Problem for Constrained Lagrangian Systems -- 5.Inverse Problem for Constrained Hamiltonian Systems -- 6.Integrability of the Constrained Rigid Body -- 7.Inverse Problem in the Vakonomic Mechanics -- Index -- Bibliography.
520 _aThis book is dedicated to study the inverse problem of ordinary differential equations, that is it focuses in finding all ordinary differential equations that satisfy a given set of properties. The Nambu bracket is the central tool in developing this approach. The authors start characterizing the ordinary differential equations in R^N which have a given set of partial integrals or first integrals. The results obtained are applied first to planar polynomial differential systems with a given set of such integrals, second to solve the 16th Hilbert problem restricted to generic algebraic limit cycles, third for solving the inverse problem for constrained Lagrangian and Hamiltonian mechanical systems, fourth for studying the integrability of a constrained rigid body. Finally the authors conclude with an analysis on nonholonomic mechanics, a generalization of the Hamiltonian principle, and the statement an solution of the inverse problem in vakonomic mechanics.
650 0 _aDifferential Equations.
650 1 4 _aOrdinary Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12147
700 1 _aRamírez, Rafael.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319263373
776 0 8 _iPrinted edition:
_z9783319263380
776 0 8 _iPrinted edition:
_z9783319799353
830 0 _aProgress in Mathematics,
_x0743-1643 ;
_v313
856 4 0 _uhttps://doi.org/10.1007/978-3-319-26339-7
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c426489
_d426489