000 03507nam a22005415i 4500
001 978-3-319-28323-4
003 DE-He213
005 20200421112555.0
007 cr nn 008mamaa
008 160302s2016 gw | s |||| 0|eng d
020 _a9783319283234
_9978-3-319-28323-4
024 7 _a10.1007/978-3-319-28323-4
_2doi
050 4 _aTA355
050 4 _aTA352-356
072 7 _aTGMD4
_2bicssc
072 7 _aTEC009070
_2bisacsh
072 7 _aSCI018000
_2bisacsh
082 0 4 _a620
_223
100 1 _aPreston, Serge.
_eauthor.
245 1 0 _aNon-commuting Variations in Mathematics and Physics
_h[electronic resource] :
_bA Survey /
_cby Serge Preston.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2016.
300 _aXIV, 235 p. 11 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aInteraction of Mechanics and Mathematics,
_x1860-6245
505 0 _aBasics of the Lagrangian Field Theory -- Lagrangian Field Theory with the Non-commuting (NC) Variations -- Vertical Connections in the Congurational Bundle and the NCvariations -- K-twisted Prolongations and -symmetries (by Works of Muriel,Romero -- Applications: Holonomic and Non-Holonomic Mechanics,H.KleinertAction Principle, Uniform Materials,and the Dissipative Potentials -- Material Time, NC-variations and the Material Aging -- Fiber Bundles and Their Geometrical Structures, Absolute Parallelism -- Jet Bundles, Contact Structures and Connections on Jet Bundles -- Lie Groups Actions on the Jet Bundles and the Systems of Differential Equations.
520 _aThis text presents and studies the method of so -called noncommuting variations in Variational Calculus. This method was pioneered by Vito Volterra who noticed that the conventional Euler-Lagrange (EL-) equations are not applicable in Non-Holonomic Mechanics and suggested to modify the basic rule used in Variational Calculus. This book presents a survey of Variational Calculus with non-commutative variations and shows that most basic properties of conventional Euler-Lagrange Equations are, with some modifications, preserved for EL-equations with K-twisted (defined by K)-variations. Most of the book can be understood by readers without strong mathematical preparation (some knowledge of Differential Geometry is necessary). In order to make the text more accessible the definitions and several necessary results in Geometry are presented separately in Appendices I and II Furthermore in Appendix III a short presentation of the Noether Theorem describing the relation between the symmetries of the differential equations with dissipation and corresponding s balance laws is presented.
650 0 _aEngineering.
650 0 _aMathematical physics.
650 0 _aMechanics.
650 0 _aVibration.
650 0 _aDynamical systems.
650 0 _aDynamics.
650 1 4 _aEngineering.
650 2 4 _aVibration, Dynamical Systems, Control.
650 2 4 _aMathematical Applications in the Physical Sciences.
650 2 4 _aMechanics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319283210
830 0 _aInteraction of Mechanics and Mathematics,
_x1860-6245
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-28323-4
912 _aZDB-2-ENG
942 _cEBK
999 _c59077
_d59077