vbid/9783319283234

Description

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� 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.Typham this is the title: Non-commuting Variations in Mathematics and Physics A Survey