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A Method For Determining Exact Stability Boundaries For Flexible Satellites With Arbitrary Position Independent Damping
Andre P. Mazzoleni* and Ian Dobson**
Abstract
Regions of parameter space can often be shown to be unstable by testing a single point of the region and using a simple continuity argument. In the case of Hamiltonian systems, and Hamiltonian systems with additional arbitrary position independent damping, the test reduces to checking the sign of the determinant of the Hessian of the Hamiltonian at a single point. Exact stability boundaries can often be simply deduced by using Liapunov s direct method to show stability on one side of the boundary and using the proposed method to show instability on the other side of the boudary. Previous studies use complete or pervasive damping assumptions to obtain exact stability boundaries while the proposed method works for no damping or arbitrary position independant damping.
*Department of Engineering, Texas Christian University, TCU Box 5100, Fort Worth, Texas 76129.
**Assistant Professor, Department of Electrical and Computer Engineering, University of Wisconsin-Madison, 1415 Johnson Drive, Madison, Wisconsin 53706.