ISSN:
1432-1467
Keywords:
gyroscopic control
;
stabilization
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Summary 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01209527
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