The Journal of Geometric Mechanics (JGM)

A unifying mechanical equation with applications to non-holonomic constraints and dissipative phenomena

Pages: 473 - 482, Volume 7, Issue 4, December 2015      doi:10.3934/jgm.2015.7.473

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E. Minguzzi - Dipartimento di Matematica e Informatica "U. Dini", Università degli Studi di Firenze, Via S. Marta 3, I-50139 Firenze, Italy (email)

Abstract: A mechanical covariant equation is introduced which retains all the effectingness of the Lagrange equation while being able to describe, in a unified way, other phenomena including friction, non-holonomic constraints and energy radiation (Lorentz-Abraham-Dirac force equation). A quantization rule adapted to the dissipative degrees of freedom is proposed which does not pass through the variational formulation.

Keywords:  Friction, non-holonomicity, Lorentz-Abraham-Dirac force.
Mathematics Subject Classification:  Primary: 70G45, 37J60; Secondary: 70F40.

Received: October 2014;      Revised: July 2015;      Available Online: October 2015.