On the Decomposition of Forces

TL;DR

This paper proves that any continuously differentiable force can be uniquely decomposed into Rayleigh and gyroscopic components, extending previous results to include piecewise differentiable forces, thereby advancing force decomposition theory.

Contribution

The paper extends existing force decomposition results to include piecewise continuously differentiable forces, providing a more general framework for force analysis.

Findings

Any continuously differentiable force decomposes into Rayleigh and gyroscopic forces.

Extension of force decomposition to piecewise continuously differentiable forces.

Improvement over previous results by David Merkin.

Abstract

We show that any continuously differentiable force is decomposed into the sum of a Rayleigh force and a gyroscopic force. We also extend this result to piecewise continuously differentiable forces. Our result improves the result on the decomposition of forces in a book by David Merkin and further extends it to piecewise continuously differentiable forces.