By Serge Preston

ISBN-10: 3319283219

ISBN-13: 9783319283210

This textual content presents

and reports the strategy of so –called noncommuting adaptations in Variational

Calculus. This method

was pioneered by way of Vito Volterra who

noticed that the conventional

Euler-Lagrange (EL-) equations aren't appropriate in Non-Holonomic Mechanics

and recommended to switch the fundamental rule

used in Variational Calculus. This book

presents a survey of Variational

Calculus with non-commutative diversifications and exhibits that most

basic homes of

conventional Euler-Lagrange

Equations are, with some

modifications, preserved for EL-equations with K-twisted

(defined via K)-variations.

Most of the

book might be understood through readers with no robust mathematical training (some

knowledge of Differential Geometry is necessary). so one can make the textual content extra obtainable the

definitions and a number of other invaluable leads to Geometry are offered separately

in Appendices I and II moreover in

Appendix III a brief presentation of the Noether Theorem

describing the relation among the

symmetries of the differential equations

with dissipation and corresponding s stability legislation is presented.