Seminar Details
2025-11-25 (14:00) : A constrained Lie group approach to the modeling of dynamic mechanical systems
At EULER (room A.002)
Organized by Mathematical Engineering
Speaker :
Olivier Bruls (University of Liège)
Abstract :
This talk addresses general-purpose geometric modeling methods for a wide class of mechanical systems which includes robotic systems, biomechanical systems, deployable space structures, automotive vehicles, or industrial machines. These systems are represented as a set of rigid and flexible bodies whose dynamics is restricted due to the presence of kinematic joints and contact conditions.
It is well-known that the motion of an isolated rigid body can be conveniently represented on the special Euclidean group SE(3). In the first part of the talk, I will show that this SE(3) representation can be extended to model deformable structures, such as rods, shells or more complex 3D flexible bodies. The Lie group framework can then be exploited for the construction of geometrically-consistent spatial discretization schemes and offers to the possibility to write the equations of motion in local frames (and not in an inertial frame).
In the second part of the talk, I will address the treatment of bilateral constraints, which model kinematic joints, leading to a formulation of the equations of motion as a differential-algebraic equation (DAE) on a Lie group. Geometric time discretization methods for such DAE will then be discussed. Notice that unilateral constraints, which model contact conditions, can also be considered by adapting the formulation of measure differential inclusions and nonsmooth time integration schemes to the Lie group settings. Finally, a few numerical examples will be presented to illustrate the generality of the proposed framework.