A Symbolic Method for the Analysis of a Nonlinear Two-Mass-Skate Model

TL;DR

This paper introduces a symbolic method to analyze the complex nonlinear dynamics of a Two-Mass-Skate model without linearization, enabling easier handling and stability analysis of the system.

Contribution

It presents a novel symbolic approach using nonlinear functions to derive explicit equations of motion for complex multibody systems like the Two-Mass-Skate.

Findings

Explicit equations of motion derived using symbolic methods

Stability analysis conducted on the nonlinear model

Method simplifies handling complex multibody dynamics

Abstract

Multibody systems usually give rise to complex nonlinear dynamics, and the bicycle is not an exception. Even a simple model as the Two-Mass-Skate presents a long expression of the kinetic energy, making difficult to write explicitly the equations of motion. Instead of linearising or approximating the model, we will overcome this issue by using a functional expression of the kinetic energy. With introduction of appropriate nonlinear functions, the equations of motion are written in a form that can be easily handled despite their complexity. A stability analysis of the dynamics is then conducted.