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

TL;DR

This paper introduces a unified covariant mechanical equation capable of describing non-holonomic constraints, dissipative phenomena, and energy radiation, providing a comprehensive framework beyond traditional Lagrangian mechanics.

Contribution

It presents a novel covariant equation that unifies the treatment of friction, non-holonomic constraints, and radiation effects in mechanics, along with a new quantization rule for dissipative systems.

Findings

Unified equation effectively describes dissipative and constrained systems

Quantization rule applicable without variational principles

Framework encompasses energy radiation 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.