# American Institute of Mathematical Sciences

December  2015, 7(4): 473-482. doi: 10.3934/jgm.2015.7.473

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

 1 Dipartimento di Matematica e Informatica "U. Dini", Università degli Studi di Firenze, Via S. Marta 3, I-50139 Firenze, Italy

Received  October 2014 Revised  July 2015 Published  October 2015

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.
Citation: E. Minguzzi. A unifying mechanical equation with applications to non-holonomic constraints and dissipative phenomena. Journal of Geometric Mechanics, 2015, 7 (4) : 473-482. doi: 10.3934/jgm.2015.7.473
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