NDLI: Controllability of a system of two symmetric rigid bodies in three space

Content Provider	IEEE Xplore Digital Library
Author	Enos, M.J.
Copyright Year	1992
Description	Author affiliation: Fields Inst. for Res. in Math. Sci., Waterloo, Ont., Canada (Enos, M.J.)
Abstract	Imposing the constraint that a mechanical system having two completely symmetric 3-D rigid bodies have zero total angular momentum, the angular velocities of these bodies are negatives of one another, and the transfer of this sytem from one position to another is nonholonomic. While Chow's theorem establishes the fixed-endpoint controllability of the system, this result does not explicitly exhibit any motions between a given set of endpoints. In the present work it is shown how to explicitly construct simple motions of this system on (0, 1) with arbitrary endpoints in SO(3)/sup 2/. In particular, using normalized quaternions to describe rotations, the author constructs, in terms of elementary functions, a continuous motion with the given endpoints; it consists of at most three successive motions during each of which the bodies rotate on fixed axes. It is assumed that the rigid bodies have coincident mass centers, that each has a completely symmetric mass distribution about its mass center, and that the inertia tensor of each body is the identity matrix.<>
Starting Page	104
Ending Page	105
File Size	217784
Page Count	2
File Format	PDF
ISBN	0780308727
DOI	10.1109/CDC.1992.371781
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1992-12-16
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Controllability Mechanical systems Angular velocity Quaternions Tensile stress Symmetric matrices
Content Type	Text
Resource Type	Article

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