Eigenvalues and eigenvectors for hybrid coordinate equations of motion for flexible spacecraft

Details Eigenvalues and eigenvectors for hybrid coordinate equations of motion for flexible spacecraft Eigenvalues and eigenvectors for hybrid coordinate equations of motion for flexible spacecraft

May 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979cemec..19..359o&link_type=abstract

Celestial Mechanics, vol. 19, May 1979, p. 359-390.

Physics

Attitude Stability, Eigenvalues, Eigenvectors, Equations Of Motion, Flexible Bodies, Spacecraft Control, Spacecraft Motion, Appendages, Minimax Technique, Structural Vibration

Scientific paper

The eigenvalues and eigenvectors of a system of linear time-invariant equations describing the attitude motion of flexible spacecraft in terms of hybrid coordinates are characterized in terms of literal expressions by using peculiar properties of the system parameter matrices. For the undamped case the eigenvalues are localized in terms of inertial matrices and modal parameters. A procedure for calculating the eigenvectors is proposed whereby the eigenproblem associated with the original system of dimension (2N + 6) is reduced to that of a symmetric and positive definite matrix of dimension N with the zero-damping assumption. The eigenvectors for systems of large dimension are obtained explicitly in terms of a 3x1 matrix whose elements are available from a system of three algebraic equations, which is provided.

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