Multibody Dynamics

Multibody systems are mechanical systems made up of multiple interconnected rigid bodies. In this course, you will learn a systematic approach for generating, solving, and integrating equations of motion used to model multibody systems.

Topics covered are:

- Three-dimensional kinematics and use of Euler angles and Tait-Bryan angles for describing orientation.

- Equations of motion for planar and three-dimensional systems, free body diagrams, constraint equations and constraint forces, uniqueness of the solution.

- Systematic approaches for generating equations of motion, e.g. Newton-Euler, Lagrange, coordinate transforms (TMT), Kane, etc.

- Relationship of maximal coordinate equations of motion to generalized coordinate equations of motion.

- Configuration (holonomic) constraints, e.g. closed kinematic loops, and motion (nonholonomic) constraints, e.g. rolling without slipping, and their relationship to degrees of freedom.

- Symbolic and numeric computational methods applicable to generating and solving equations of motion.

- Numerical integration of coupled differential and differential algebraic equations with careful attention to stability, accuracy, and minimization of integration drift.

- Visualization and analysis of two- and three-dimensional motion.