Program Overview

Multibody and Non-Linear Dynamics

Course Description

Multibody dynamics relates to the modeling and analysis of the dynamic behavior of multibody systems. Multibody systems are mechanical systems that consist of multiple, mutually connected bodies. Here, only rigid bodies will be considered. Many industrial systems, such as robots, cars, truck-trailer combinations, motion systems, etc., can be modeled using techniques from multibody dynamics. The analysis of the dynamics of these systems can support both the mechanical design and the control design for such systems. This course focuses on the modeling and analysis of multibody systems.

Most dynamical systems, such as mechanical (multibody) systems, exhibit nonlinear dynamical behavior to some extent. Examples of nonlinearities in mechanical systems are: geometric nonlinearities, hysteresis, friction, and many more. This course focuses on the effects that such nonlinearities have on the dynamical system behavior. In particular, a key focal point of the course is the in-depth understanding of stability of equilibrium points and periodic orbits for nonlinear dynamical systems. These tools for the analysis of nonlinear systems are key stepping stones towards the control of nonlinear, robotic, and automotive systems, which are topics treated in other courses in the ME MSc curriculum.

Course Topics

• Kinematics and dynamics of a single free rigid body in three-dimensional space
• Bilateral kinematic constraints and the 3D-dynamics of a single rigid body subject to such constraints
• Kinematics and dynamics of multibody systems
• Analysis of the dynamic behavior of multibody systems by means of both simulation techniques and linearization techniques
• Analysis of phase portraits of 2-dimensional dynamical systems
• Fundamentals and mathematical tools for nonlinear differential equations
• Lyapunov stability, passivity, Lyapunov functions as a tool for stability analysis
• Bifurcations, parameter-dependency of equilibrium points and period orbits

Objectives

• Understand the relevance of multibody and nonlinear dynamics in the broader context of mechanical engineering
• Understand fundamental principles in dynamics
• Create models for the kinematics and dynamics of a single free rigid body in three-dimensional space and model the mass geometry of a body in 3D space
• Create models for bilateral kinematic (holonomic and non-holonomic) constraints and models for the 3D-dynamics of a single rigid body subject to such constraints
• Create models for the kinematics and dynamics of multibody systems in 3D space
• Analyse the kinematics and dynamics of multibody systems through simulation and linearization techniques
• Understand the fundamental differences between linear and nonlinear dynamical systems
• Analyse phase portraits of two-dimensional nonlinear systems
• Perform stability analysis of equilibria of nonlinear systems using tools from Lyapunov stability theory
• Understand the concept of passivity of mechanical systems and its relation with the notion of stability
• Analyse elementary bifurcations of equilibria of nonlinear systems

Method of Assessment

Written examination

Course Period and Format

• Course period: 1/09/15 31/08/26
• Course format: Course