000 03061nam a22004695i 4500
001 978-3-540-46441-9
003 DE-He213
005 20160624101823.0
007 cr nn 008mamaa
008 121227s1991 gw | s |||| 0|eng d
020 _a9783540464419
_9978-3-540-46441-9
024 7 _a10.1007/BFb0097544
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515
_223
100 1 _aMielke, Alexander.
_eauthor.
245 1 0 _aHamiltonian and Lagrangian Flows on Center Manifolds
_h[electronic resource] :
_bwith Applications to Elliptic Variational Problems /
_cby Alexander Mielke.
260 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1991.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1991.
300 _aX, 140 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1489
505 0 _aNotations and basic facts on center manifolds -- The linear theory -- Hamiltonian flows on center manifolds -- Hamiltonian systems with symmetries -- Lagrangian systems -- Nonautonomous systems -- Elliptic variational problems on cylindrical domains -- Capillarity surface waves -- Necking of strips -- Saint-Venant's problem.
520 _aThe theory of center manifold reduction is studied in this monograph in the context of (infinite-dimensional) Hamil- tonian and Lagrangian systems. The aim is to establish a "natural reduction method" for Lagrangian systems to their center manifolds. Nonautonomous problems are considered as well assystems invariant under the action of a Lie group ( including the case of relative equilibria). The theory is applied to elliptic variational problemson cylindrical domains. As a result, all bounded solutions bifurcating from a trivial state can be described by a reduced finite-dimensional variational problem of Lagrangian type. This provides a rigorous justification of rod theory from fully nonlinear three-dimensional elasticity. The book will be of interest to researchers working in classical mechanics, dynamical systems, elliptic variational problems, and continuum mechanics. It begins with the elements of Hamiltonian theory and center manifold reduction in order to make the methods accessible to non-specialists, from graduate student level.
650 0 _aMathematics.
650 0 _aGlobal analysis (Mathematics).
650 1 4 _aMathematics.
650 2 4 _aAnalysis.
650 2 4 _aTheoretical, Mathematical and Computational Physics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540547105
786 _dSpringer
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1489
856 4 0 _uhttp://dx.doi.org/10.1007/BFb0097544
942 _2EBK1411
_cEBK
999 _c30705
_d30705