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
Hall, Christopher D. Committee Chair
Cliff, Eugene M. Committee Member
Hendricks, Scott L. Committee Member
Kraige, Luther Glenn Committee Member
Lutze, Frederick H. Jr. 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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