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An Approximate Solution For The Spinup Dynamics Of Near Axisymmetric Axial Gyrostats Using The Method Of Multiple Scales, Stewart J. Kowall
An Approximate Solution For The Spinup Dynamics Of Near Axisymmetric Axial Gyrostats Using The Method Of Multiple Scales, Stewart J. Kowall
Theses and Dissertations
Approximate solutions for the spinup of a near axisymmetric gyrostat are derived using the straightforward expansion method and the method of multiple scales. Two method of multiple scale solutions are presented. The first is derived using cartesian coordinates while the second is derived using cylindrical coordinates. The multiple scales solutions are compared to numerically integrated results for oblate and prolate configurations. A comparison for flat spin recovery is also accomplished. Excellent results are obtained for oblate configurations. Trajectory separatrix crossings hindered the results for prolate configurations and flat spin recoveries.
The Modal Solution To The Moon's Orbit Using Canonical Floquet Perturbation Theory, Kurt A. Vogel
The Modal Solution To The Moon's Orbit Using Canonical Floquet Perturbation Theory, Kurt A. Vogel
Theses and Dissertations
Using the restricted three body problem, the equations of motion EOM and Hamiltonian are computed for the moons orbit in physical variables. A periodic orbit is found in the vicinity of the moons orbit, and classical Floquet theory is applied to the periodic orbit to give stability information and the complete solution to the equations of variation. Floquet theory also supplies a transformation from physical variables to modal variables. This transformation to modal variables is made canonical by constraining the initial transformation matrix to be symplectic. Actual lunar data is used to calculate the modes for the real moons orbit. …