A stationarity principle for the eigenvalue problem for rotating structures
Abstract
An important question associated with the eigenvalue problem for flexible gyroscopic systems is that of discretization of continuous elastic members. If discretization is performed by the assumed modes method, the question arises as to the type of functions to be used in series expansions. In particular, the question is whether one should use rotatingappendage eigenfunctions, fixedbase eigenfunctions, or any other set of admissible functions. The answer to this question is provided by a stationarity principle for rotating structures developed and proved in this paper. On the basis of this principle, it can be concluded that discretization by means of admissible functions is quite sufficient, provided the set of admissible functions is complete, and the use of appendage eigenfunctions is unnecessary. The principle has important implications not only in a modal analysis for the response but also in a stability analysis of flexible spacecraft.
 Publication:

AIAA, Aerospace Sciences Meeting
 Pub Date:
 January 1976
 Bibcode:
 1976aiaa.meetU....M
 Keywords:

 Discrete Functions;
 Eigenvalues;
 Finite Element Method;
 Flexible Bodies;
 Rotary Gyroscopes;
 Eigenvectors;
 Linearization;
 Matrices (Mathematics);
 RayleighRitz Method;
 Resonant Frequencies;
 Rigid Structures;
 Spacecraft Stability;
 Astrodynamics