Rayleigh's dissipation function at work

TL;DR

This paper demonstrates how Rayleigh's dissipation function can be effectively used to solve mechanical problems involving velocity-dependent friction, simplifying the process to basic calculations of energy and dissipation.

Contribution

It introduces a simple integral expression for the Rayleigh dissipation function based on contact surface analysis, facilitating easier solutions of Lagrangian problems with friction.

Findings

Simplified method for calculating dissipation function in frictional problems

Reduction of complex friction problems to elementary energy calculations

Examples illustrating pedagogical applications of the method

Abstract

It is shown that the Rayleigh's dissipation function can be successfully applied in the solution of mechanical problems involving friction non-linear in the velocities. Through the study of surfaces at contact we arrive at a simple integral expression which gives directly the Rayleigh dissipation function in terms of generalized coordinates. In this way the solutions of Lagrangian problems with friction are reduced to often elementary calculations of the kinetic energy, the potential energy and the Rayleigh dissipation function. Some examples of pedagogical interest are given.