Non-commuting Variations in Mathematics and Physics A Survey /

• Main Author: Preston, Serge (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: Interaction of Mechanics and Mathematics,
• Subjects: Engineering.; Mathematical physics.; Mechanics.; Vibration.; Dynamical systems.; Dynamics.; Vibration, Dynamical Systems, Control.; Mathematical Applications in the Physical Sciences.

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 us...

Table of Contents:

• Basics 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.