The Shape-Triangle

  • Peter Chr. Müller
Part of the International Centre for Mechanical Sciences book series (CISM, volume 63)


The stability of gyroscopic devices or satellites often only depends on the mass geometry of these bodies, i.e. on their moments of inertia. Thus, a gravity-gradient stabilized satellite on a circular orbit around the earth has a stable position only if the principal moments of inertia A, B, C satisfy the condition
or the conditions
(notation and detailed discussion see [1]).Relation (1.1.2b) especially shows that the statement of stability conditions requires a suitable presentation of the moments of inertia. Fundamentally the mass geometry can be described in a three dimensional parameter space where the principal moments of inertia are the ordinates of a set of rectangular axes. But there are two disadvantages; firstly, the nonplanar description is cumbersome and un-illustrative and, secondly, this description bears no relation to the special type of the stability conditions. The degree of stability does not depend on A, B, C but only on the ratio A: B: C. There are two essential parameters only and therefore the stability regions can be registered in two -dimensional parameter spaces.


Rigid Body Circular Orbit Instability Region Middle Line Coordinate Line 
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Copyright information

© Springer-Verlag Wien 1972

Authors and Affiliations

  • Peter Chr. Müller
    • 1
  1. 1.Technical University of MunichGermany

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