Vibration of a flexible spacecraft with momentum exchange controllers

Canavin, J. R.

Floating reference frames were investigated in order to allow first order vibration analysis in the presence of large system rotations. When the deformations of an elastic continuum are expanded in terms of the free-free modes of an unconstrained system, the rigid body modes are found to be fixed relative to the Tisserand frame, with respect to which the relative momentum is zero. The proof presented for this is based on the orthogonality condition for modes with distinct natural frequencies. This result also guarantees the independence of coordinates for all modes with nonzero natural frequencies. A Modified Tisserand Constraint is introduced in order to define a floating reference frame with similar properties for an elastic body which contains a spinning rotor. Finite element equations of motion are derived for a completely flexible spacecraft with momentum exchange controllers, using a Modified Tisserand Frame. The deformable systems covered in this application are assumed to undergo only small rotations, and therefore the rotor torques must formally be small, although in engineering applications it may be possible to relax this constraint. A modal analysis is performed for the system and the resulting set of equations is reduced in number by a truncation procedure for more efficient system simulation.

Document ID

19770004153

Acquisition Source

Legacy CDMS

Document Type

Contractor Report (CR)

Authors

Date Acquired

September 3, 2013

Publication Date

June 1, 1976

Subject Category

Report/Patent Number

Accession Number

77N11096

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Distribution Limits

Public

Work of the US Gov. Public Use Permitted.

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