Long-time simulation for a rigid body

Version 1.1.0.0 (8.65 KB) by Giulia Ortolan
Implementation of Lie group methods for the dynamics of a rigid body.
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Updated 2 Jun 2010

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These function implement Lie integrators to perform long time simulation of a rigid body in a static spring-magnetic potential field. This numerical test of symplecticity is detailed in:

Bou-Rabee, N., Ortolan, G., and Saccon, A. [2010].
A counterexample showing the semi-explicit Lie-Newmark algorithm is not variational. (preprint).

Results show the following:
(i) VLV algorithm exhibits no energy drift;
(ii) Lie-Newmark algorithm exhibits energy drift; and,
(iii) `explicit' Lie-Midpoint algorithm exhibits energy drift.

File details:
- basicrunem.m: launches the Lie methods;
- NMB.m: semi-explicit Lie-Newmark algorithm;
- LIEMIDEA.m: explicit Lie-Midpoint algorithm;
- VLV.m: Lie-Verlet algorithm;
- wedge.m: hat map.

Cite As

Giulia Ortolan (2024). Long-time simulation for a rigid body (https://www.mathworks.com/matlabcentral/fileexchange/27792-long-time-simulation-for-a-rigid-body), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2009b
Compatible with any release
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes
1.1.0.0

Corrected bug at line 117 of NMB.m.
1.0.0.0