Quaternion Variational Integrators Paper04 Feb 2016
I was just notified that my first journal paper, “Quaternion Variational Integrators for Spacecraft Dynamics,” which was accepted for publication in the AIAA Journal of Guidance, Control, and Dynamics back in April of last year, will be appearing in print in the next issue. In the paper I develop special-purpose numerical integration algorithms for simulating spacecraft attitude dynamics. The algorithms are derived by discretizing Hamilton’s Principle (also known as the “Principle of Least Action” or “Principle of Stationary Action”) and have several interesting properties, including long-term energy and momentum conservation (for conservative systems). Here’s a plot from a simulation of a tumbling rigid body comparing the energy drift between the 2nd order midpoint rule, MATLAB’s ODE45 integrator, and the variational integrator in the paper:
If you’re still with me after all of that jargon, you can check out the paper on the journal’s website or download a preprint here. I’m also posting MATLAB implementations of the integrators and some demos on GitHub.