Produktbild: Non-commuting Variations in Mathematics and Physics

Non-commuting Variations in Mathematics and Physics

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A Survey, Interaction of Mechanics and Mathematics

ISBN: 3319283219
ISBN 13: 9783319283210
Autor: Preston, Serge
Verlag: Springer Verlag GmbH
Umfang: xiv, 235 S., 11 s/w Illustr., 235 p. 11 illus.
Erscheinungsdatum: 11.03.2016
Auflage: 1/2016
Format: 2 x 24 x 16
Gewicht: 532 g
Produktform: Kartoniert
Einband: Kartoniert

This 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 EulerLagrange (EL) equations are not applicable in NonHolonomic 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.

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