Gyroscopic control and stabilization
Journal
Journal of Nonlinear Science
Journal Volume
2
Journal Issue
4
Pages
367-415
Date Issued
1992
Author(s)
Abstract
In this paper, we consider the geometry of gyroscopic systems with symmetry, starting from an intrinsic Lagrangian viewpoint. We note that natural mechanical systems with exogenous forces can be transformed into gyroscopic systems, when the forces are determined by a suitable class of feedback laws. To assess the stability of relative equilibria in the resultant feedback systems, we extend the energy-momentum block-diagonalization theorem of Simo, Lewis, Posbergh, and Marsden to gyroscopic systems with symmetry. We illustrate the main ideas by a key example of two coupled rigid bodies with internal rotors. The energy-momentum method yields computationally tractable stability criteria in this and other examples. © 1992 Springer-Verlag New York Inc.
SDGs
Type
journal article