Effects of Flexibility on Stability
We are interested in the attitude of the space vehicle with respect to a rotating reference frame. For a gravity stabilized vehicle this re ference will be the orbital frame with one axis per pendicular to the plane of the orbit and a second axis aligned
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Pierre Y. WILLEMS Institut de Mecanique Uriiversite de Louvain
Jens WITIENBURG Lehrstuhl und lnstitut fiir Mechanik Technische Hochschule Hannover
INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES C 0 U RS E S A N D
L E C T U R E S - No. 102
ROBERT ROBERSON UNIVERSITY OF CALIFORNIA,
SAN
DIEGO
PIERRF. WILLEMS UNIVEHSITE
CA1'HOLIQFE, LOUVAIN
JENS WITTENBURG TECHNISCHE
UNIVERSITAT,
HANNOVER
ROTATIONAL DYNAMICS OF ORBITING GYROSTATS
DEPARTMENT OF GENERAL MECHANICS COURSE HELD IN DUBROVNIK SEPTEMBER 1971
UDINE 1971
SPRINGER-VERLAG WIEN GMBH
This work is sub.iect to copyright.
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are
reserved,
whether the whole or part of the material is concemed specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks.
©
1972 by Springer-Verlag Wien
Originally published by Springer-Verlag Wien-New York in 1972
ISBN 978-3-211-81198-6 DOI 10.1007/978-3-7091-2930-2
ISBN 978-3-7091-2930-2 (eBook)
P R E F A C E At the suggestion of Prof. Sobrero of CISM I organized a series of lectures to be presented by me and several colleagues at Dubrovnik in September 1971 under the joint auspices of CISM and the University of Zagreb. For his encouragement and support, I wish to immediately express my thanks. The lectures were organized in two series, and three hours of lectures were presented in each series each day during 13 - 17 September. This book contains the lectures of the first series, given by the undersigned, Dr. Pierre Y.
Willems and Dr. Jens
Wittenburg. Each series was devoted to one aspect of special current importance relating to the rotational behaviour of spacecraft. The subject of this first series was the rotational dynamics of orbiting gyrostats. Two topics were emphasized,
for these two underlie the major
technological applications involving spinning gyrostatic spacecraftand gyrostatic spacecraft in equilibrium states under the action of gravitational torque. The first problem is to establish the conditions under which a gyrostat can spin freely in space without being subject to any torque, and to develop complete $0lutions in terms of elliptic functions for the spinning motion of a special kind of gyrostat in which the in-
Preface
4
ternal angular momentum is aligned with a principal axis of inertia. The second problem is to establish the nature of a gyrostat's gravitational equilibrium orientations and their stability. Technological opplications build on these problems in pure rotational dynamics by introducing dissipative mechanisms~ a subject not covered in these lectures. However~ as intermediate ground between this series of lectures and the companion one on spacecraft flexibility~ the effect of flexibility on the stability of gravitational equilibria is included here. Dr. Wittenburg prepared and presented Lectures 6 and 7~ Dr. Willems Lectures 11 and 12~ and I the remaining lectures
Dubrovnik~
September 1971
1. Introductory Remarks
The subject of rotational dynamics was born
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