A variational approach to the analysis of non-conservative mechatronic systems

TL;DR

This paper introduces a systematic variational method for deriving equations of motion in dissipative mechatronic systems, unifying mechanical and electrical analysis without ad hoc assumptions, enabling automation and broader applicability.

Contribution

It presents a novel variational framework that generalizes potentials for dissipative elements, allowing unified analysis of energy and power in mechanical and electrical systems.

Findings

Derived equations of motion for typical mechatronic systems

Unified treatment of conservative and non-conservative forces

Method suitable for automation with algebra software

Abstract

We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical and, mechatronic systems. We derive the equations of motion for some typical mechatronic systems using deterministic principles that are strictly variational. We do not use any ad hoc features that are added on after the analysis has been completed, such as the Rayleigh dissipation function. We generalise the concept of potential, and define generalised potentials for dissipative lumped system elements. Our innovation offers a unified approach to the analysis of mechatronic systems where there are energy and power terms in both the mechanical and electrical parts of the system. Using our novel technique, we can take advantage of the analytic approach from mechanics, and we can apply these pow- erful analytical methods to electrical and to mechatronic systems. We can analyse systems that include non-conservative forces. Our methodology is deterministic and does does require any special intuition, and is thus suitable for automation via a computer-based algebra package.