WORKSHOP Rigid body and rod dynamics: modeling and simulation.
The workshop will be held in the room 656 SIMASTUEN in Sentralbygg II, 6th floor. From 10:15 to 13:00. This workshop is the kick off meeting for the activities of the Special Interest Group in "Control with geometric modeling and simulation methods".
Speakers
- Gilles Villmart, University of Geneva
- Niklas Säfström IMF (NTNU)
- Gullik Jensen ITK/CeSOS (NTNU)
We consider numerical simulation of rigid body dynamics and related models of rod dynamics. We are interested in numerical methods which respect the geometric structure of the underlying equations and their performance in real life simulations and in particular modeling and control of offshore pipelay operations.
A simple lunch will be served after the lectures.
Programme
| Time | Activity | comments |
|---|---|---|
| 10:15 | Lecture by Gilles Vilmart | see abstract below |
| 11:00 | Lecture by Gullik Jensen | see abstract below |
| 11:30 | Lecture by Niklas Säfström | see abstract below |
| 12:00 | Lunch | informal discussion on the activity of the SIG |
| 12:45 | Conclusion |
Gilles Vilmart
On modifying integrators and rigid body dynamics
(This is joint work with Philippe Chartier and Ernst Hairer)
The Discrete Moser-Veselov algorithm is an excellent geometric integrator for the motion of the free rigid body. It is symplectic and time-reversible, and it conserves all first integrals of the system. The only drawback is its low order of convergence. We present a modification of this algorithm to arbitrarily high-order which has negligeable overhead but considerably improves the accuracy.
This modification is inspired by the theory of modified differential equations (backward error analysis) for the study of geometric integrators for ordinary differential equations. We present the generalization of this idea and introduce modifying integrators, a new approach to high-order, structure-preserving numerical integrators.
Gullik Jensen
Modeling and Control of Offshore Pipelay Operations Based on a Finite Strain Pipe Model
This talk deals with modeling and control of offshore pipelay operations from a dynamically positioned surface vessel where a nonlinear dynamic beam formulation in three dimensions capable of undergoing shearing, twist and bending is used to model the pipe. This pipe model is coupled with a nonlinear vessel model that has been adopted as a standard for vessel control design and analysis purposes. The complete pipelay system is shown to be input-output passive taking the thruster force as the input and the vessel velocity as the output. A nonlinear controller is applied, and using the passivity condition of feedback connection of two passive systems, the closed loop system is stable. Numerical simulations using both PD and PID controllers illustrate the theoretical results.
Niklas Säfström
A multi-symplectic formulation of an elastic rod model by J.C. Simo
We will discuss a multi-symplectic formulation of the elastic rod model formulated by J. C. Simo. The elastic rod model is written as constraint Hamiltonian PDE as well as in a constraint multi-symplectic formulation in terms of quaternions. We also look at some relations between the elastic rod model and the quaternionic formulation of rigid body dynamics.