A Computational Approach for Variational Integration of Attitude Dynamics on SO(3)

2022/01/03 by Nikhil Potu Surya Prakash, Prakash, Nikhil Potu Surya
Engineering · #Dynamics and Control of Mechanical Systems #Control and Dynamics of Mobile Robots #Fluid Dynamics Simulations and Interactions

paper · pdf · doi:10.48550/arxiv.2201.00713

Abstract

In this article, a brief description of Discrete Mechanics and Variational Integrators which preserve the symplectic structure of the flow will be provided and a Newton-Raphson algorithm that can be used to solve implicit equations on the SO(3) manifold will be developed. These techniques will be used to simulate the rotational dynamics of a rigid body evolving on the Lie Group SO(3).

Related

• The SO(3) and SE(3) Lie Algebras of Rigid Body Rotations and Motions and their Application to Discrete Integration, Gradient Descent Optimization, and State Estimation
• Geometric Tracking Control of the Attitude Dynamics of a Rigid Body on SO(3)
• Global Symplectic Uncertainty Propagation on SO(3)
• Optimal Attitude Control of a Rigid Body using Geometrically Exact Computations on SO(3)
• Propagation of Uncertainty in Rigid Body Attitude Flows