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

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.

Latex2e, 10 pages. V2: some corrections in Sect. 3

References in corpus (4)

• The classical mechanics of non-conservative systems
• Rayleigh's dissipation function at work
• Inverted Oscillator
• From Classical Mechanics with Doubled Degrees of Freedom to Quantum Field Theory for Nonconservative System