Learning objectives

The course will give an overview on the main techniques for modeling rigid multibody systems through Ordinary Differential Equations (ODE) and Differential-Algebraic Equations (DAE). Further, numerical simulation methods for rigid multibody systems will be presented through MATLAB and a commercial software. The numerical integration schemes for the equations of motion for the forward dynamics simulation of multibody systems modeled through Differential-Algebraic Equations (DAE) will be discussed highlighting the related issues. The numerical methods discussed during the course will be tested in MATLAB/Simulink.
The training objectives are:
- understanding of the techniques for modeling multibody systems;
- critical ability to compare them;
- ability to implement a multibody simulator in MATLAB/Simulink environment;
- critical ability to analyze the results according to the chosen implementation.

Prerequisites and basic notions

Fundamentals of physics, fundamentals of mathematics and linear algebra, MATLAB programming

Program

1) Overview of mechanical systems, components and motion.
2) Review of basic methods for modeling rigid multibody systems through DAEs
3) Overview of the numerical methods for converting the DAEs into ODEs and for the simulation of rigid multibody systems
4) Overview of the numerical integration schemes for multibody systems.
5) Discussion of the numerical issues in the forward dynamics simulation of multibody systems.
6) Implementation of sample models and application of the numerical simulation methods in MATLAB
7) Introduction of the advanced state-of-the-art methods for the improvement of the accuracy of multibody system simulations.
8) Introduction to a commercial multibody simulator and implementation of some sample multibody systems.

Bibliography

Didactic methods

Traditional lectures with hands-on experiences with a personal PC.

Learning assessment procedures

Individual project related to personal PhD topics

Assessment

Participation in lessons and discussions and discussion of the project.

Criteria for the composition of the final grade

Adequate/Insufficient.

Scheduled Lessons

Sustainable Development Goals - SDGs

This initiative contributes to the achievement of the Sustainable Development Goals of the UN Agenda 2030. More information on sustainability