Non-commuting Variations in Mathematics and Physics: A Survey: Interaction of Mechanics and Mathematics
Autor Serge Prestonen Limba Engleză Paperback – 11 mar 2016
Most of thebook can be understood by readers without strong mathematical preparation (someknowledge of Differential Geometry is necessary). In order to make the text more accessible thedefinitions and several necessary results in Geometry are presented separatelyin Appendices I and II Furthermore inAppendix III a short presentation of the Noether Theoremdescribing the relation between thesymmetries of the differential equationswith dissipation and corresponding s balance laws is presented.
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Specificații
ISBN-13: 9783319283210
ISBN-10: 3319283219
Pagini: 230
Ilustrații: XIV, 235 p. 11 illus.
Dimensiuni: 155 x 235 x 16 mm
Greutate: 0.36 kg
Ediția:1st ed. 2016
Editura: Springer International Publishing
Colecția Springer
Seria Interaction of Mechanics and Mathematics
Locul publicării:Cham, Switzerland
ISBN-10: 3319283219
Pagini: 230
Ilustrații: XIV, 235 p. 11 illus.
Dimensiuni: 155 x 235 x 16 mm
Greutate: 0.36 kg
Ediția:1st ed. 2016
Editura: Springer International Publishing
Colecția Springer
Seria Interaction of Mechanics and Mathematics
Locul publicării:Cham, Switzerland
Public țintă
ResearchCuprins
Basics of the Lagrangian FieldTheory.- Lagrangian Field Theory with the Non-commuting (NC)Variations.- Vertical Connections in the Congurational Bundle and theNCvariations.- K-twisted Prolongations and -symmetries (by Works ofMuriel,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 GeometricalStructures, Absolute Parallelism.- Jet Bundles, Contact Structures andConnections on Jet Bundles.- Lie Groups Actions on the Jet Bundles and theSystems of Differential Equations.
Textul de pe ultima copertă
This text presentsand studies the method of so –called noncommuting variations in VariationalCalculus. This methodwas pioneered by Vito Volterra whonoticed that the conventional Euler-Lagrange (EL-) equations are not applicable in Non-Holonomic Mechanicsand suggested to modify the basic ruleused in Variational Calculus. This book presents a survey of VariationalCalculus with non-commutative variations and shows that most basic properties of conventional Euler-LagrangeEquations are, with somemodifications, preserved for EL-equations with K-twisted (defined by K)-variations.
Most of thebook can be understood by readers without strong mathematical preparation (someknowledge of Differential Geometry is necessary). In order to make the text more accessible thedefinitions and several necessary results in Geometry are presented separatelyin Appendices I and II Furthermore inAppendix III a short presentation of the Noether Theoremdescribing the relation between thesymmetries of the differential equationswith dissipation and corresponding s balance laws is presented.
Most of thebook can be understood by readers without strong mathematical preparation (someknowledge of Differential Geometry is necessary). In order to make the text more accessible thedefinitions and several necessary results in Geometry are presented separatelyin Appendices I and II Furthermore inAppendix III a short presentation of the Noether Theoremdescribing the relation between thesymmetries of the differential equationswith dissipation and corresponding s balance laws is presented.
Caracteristici
A survey of non-commuting Variations in Mathematics and Physics Presents and develops methods of analysis, potential classification and of study of dissipative patterns of behavior using classical methods of differential geometry and variational calculus Presents a large number of examples of geometrical description of different dynamical behavior in the evolutional systems of partial and ordinary differential equations and characteristics of their irreversible behavior Demonstrates that a large variety of irreversible dynamical behavior in physical, mechanical, etc. systems is covered by the Lagrangian formalism with non-commutative variations Includes supplementary material: sn.pub/extras