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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 674910, 11 pages
http://dx.doi.org/10.1155/2014/674910
Research Article

Formulation and Simulations of the Conserving Algorithm for Feedback Stabilization on Rigid Body Rotations

1Department of Occupational Safety and Health, Chang Jung Christian University, Tainan City 71101, Taiwan
2Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455-0170, USA

Received 19 February 2014; Accepted 29 March 2014; Published 27 April 2014

Academic Editor: Her-Terng Yau

Copyright © 2014 Yong-Ren Pu and Thomas A. Posbergh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The problem of stabilization of rigid bodies has received a great deal of attention for many years. People have developed a variety of feedback control laws to meet their design requirements and have formulated various but mostly open loop numerical algorithms for the dynamics of the corresponding closed loop systems. Since the conserved quantities such as energy, momentum, and symmetry play an important role in the dynamics, we investigate the conserved quantities for the closed loop control systems which formally or asymptotically stabilize rigid body rotation and modify the open loop numerical algorithms so that they preserve these important properties. Using several examples, the authors first use the open loop algorithm to simulate the tumbling rigid body actions and then use the resulting closed loop one to stabilize them.