Gravitational friction from d'Alembert's principle

TL;DR

This paper investigates gravitational friction caused by non-holonomic constraints in a medium, deriving energy loss from first principles and confirming results with continuum mechanics, thus extending the understanding of dissipative gravitational effects.

Contribution

It introduces a novel analysis of gravitational friction using d'Alembert's principle for non-holonomic constraints, linking virtual work and continuum mechanics approaches.

Findings

Energy loss due to gravitational interaction is quantified from first principles.

The dissipative nature of gravitational friction is established.

Results are consistent with continuum mechanics and stress principles.

Abstract

The least action principle played a central role in the development of modern physics. A major drawback of the principle is that its applicability is limited to holonomic constraints. In the present work, we investigate the energy lost by particles as a result of the gravitational interaction in a homogeneous low-density medium subject to non-holonomic constraints. We perform the calculation for an arbitrary particle and outline the specific result for photons. The energy lost is calculated from first principles based on the principle of virtual work and the d'Alembert principle. Under the formalism mentioned above, the dissipative nature of the effect is established. Furthermore, we show that the results agree with an alternative derivation based on continuum mechanics and the Euler-Cauchy stress principle.