Dynamics of multibody systems

Short description: The course will largely follow the description in Shabana's book in describing dynamical systems of bodies using co-rotating reference frames. This approach is beneficial over using generalized coordinates in a Lagrangian/Hamiltonian fashion¹ because of the relative simplicity with which it allows for generalization. Programs such as ADAMS use variants of this precisely because of this versatility. The drawback of the approach is that in the derivation, the constraint equations connecting different bodies together appear as explicit constraint equations, which results in a set of differential-algebraic equations for which dedicated solution methods must be used. Describing the theory behind this will be the lion share of the material discussed during the weekly recurring lecture.

In this course, students will build a framework for multibody simulations with bodies exhibiting small deformations about an undeformed setting by collaborative and competitive programming assignments. The idea is for different solution techniques to be evaluated with respect to each other.

Formalities: The programming language used will be discussed during a preliminary meeting, butis leaning towards Matlab. The schedule will also be set at the preliminary meeting. This first meeting, thus obviously important, will be held Friday the 13th of February at 14:00 in TM room Newton.

¹see e g Hand and Finch, Analytical Mechanics, 1998 or the course compendium in Rigid body dynamics MMA092 for further descriptions of this approach.