Abstract
In Multibody System Dynamics 2, 71–88, wedescribed the Munthe-Kaas and Crouch–Grossman methods for integratingordinary differential equations numerically on Lie groups. We used theheavy top as a special test problem, and showed that the numericalsolution respects the configuration space TSO(3). We were, however, notable to generate numerical solutions that preserved the first integralsof the top. In this paper, we formulate the heavy top equations on amore natural configuration space, and show that both the Munthe-Kaas andthe Crouch–Grossman methods with suitable coefficient sets can generatenumerical solutions that render first integrals to machine accuracy. Asa partial answer to the comment in 'Concluding Remarks' inMultibody System Dynamics 2, 71–88, we also argue that forHamiltonian systems on the dual space of a Lie algebra, theinfinitesimal generator map describing the differential equation for thecoadjoint action is the functional derivative of the Hamiltonian.
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Engø, K., Marthinsen, A. A Note on the Numerical Solution of the Heavy Top Equations. Multibody System Dynamics 5, 387–397 (2001). https://doi.org/10.1023/A:1011459217639
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DOI: https://doi.org/10.1023/A:1011459217639