| dc.description.abstract |
<p>Rolling Isolation Systems provide a simple and effective means for protecting components
from horizontal floor vibrations. In these systems a platform rolls on four steel
balls which, in turn, rest within shallow bowls. The trajectories of the balls is
uniquely determined by the horizontal and rotational velocity components of the rolling
platform, and thus provides nonholonomic constraints. In general, the bowls are not
parabolic, so the potential energy function of this system is not quadratic. This
thesis presents the application of Gauss's Principle of Least Constraint to the modeling
of rolling isolation platforms. The equations of motion are described in terms of
a redundant set of constrained coordinates. Coordinate accelerations are uniquely
determined at any point in time via Gauss's Principle by solving a linearly constrained
quadratic minimization. In the absence of any modeled damping, the equations of motion
conserve energy. This mathematical model is then used to find the bowl profile that
minimizes response acceleration subject to displacement constraint.</p>
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