Title page for ETD etd-07202001-122347

Type of Document

Dissertation

Author

Sandfry, Ralph Anthony

URN

etd-07202001-122347

Title

Equilibria of a Gyrostat with a Discrete Damper

Degree

PhD

Department

Aerospace and Ocean Engineering

Advisory Committee

Advisor Name	Title
Dr. Christopher D. Hall	Committee Chair
Dr. Eugene M. Cliff	Committee Member
Dr. Frederick H. Lutze	Committee Member
Dr. L. Glenn Kraige	Committee Member
Dr. Scott L. Hendricks	Committee Member

Keywords

gyrostat
satellite
dual-spin
bifurcation
damping

Date of Defense

2001-07-09

Availability

unrestricted

Abstract

We investigate the relative equilibria of a gyrostat with a
spring-mass-dashpot damper to gain new insights into the dynamics
of spin-stabilized satellites. The equations of motion are
developed using a Newton-Euler approach, resulting in equations in
terms of system momenta and damper variables. Linear and nonlinear
stability methods produce stability conditions for simple spins
about the nominal principal axes. We use analytical and numerical
methods to explore system equilibria, including the bifurcations
that occur for varying system parameters for varying rotor
momentum and damper parameters. The equations and bifurcations
for zero rotor absolute angular momentum are identical to those
for a rigid body with an identical damper. For the more general
case of non-zero rotor momentum, the bifurcations are complex
structures that are perturbations of the zero rotor momentum case.
We examine the effects of spring stiffness, damper position, and
inertia properties on the global equilibria. Stable equilibria
exist for many different spin axes, including some that do not lie
in the nominally principal planes. Some bifurcations identify
regions where a jump phenomenon is possible. We use
Liapunov-Schmidt reduction to determine an analytic relationship
between parameters to determine if the jump phenomenon occurs.
Bifurcations of the nominal gyrostat spin are characterized in
parameter space using two-parameter continuation and the
Liapunov-Schmidt reduction technique. We quantify the effects of
rotor or damper alignment errors by adding small displacements to
the alignment vectors, resulting in perturbations of the
bifurcations for the standard model. We apply the global
bifurcation results to several practical applications. We relate
the general set of all possible equilibria to specific equilibria
for dual-spin satellites with typical parameters. For systems
with tuned dampers, where the natural frequency of the
spring-mass-damper matches the gyrostat precession frequency, we
show numerically and analytically that the existence of certain
equilibria are related to the damper tuning condition. Finally,
the global equilibria and bifurcations for varying rotor momentum
provide a unique perspective on the dynamics of simple rotor
spin-up maneuvers.

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