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Try the following questions… Suppose C
is the centroidal curve associated with rolling a
piecewise smooth convex wheel along a flat straight path. Recall the
correspondence between |
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for the
parameterizations of the centroidal curve C and the boundary of the original
wheel. Show
that local minimums on C correspond
to stable balancing points. Show that local maximums on C correspond to unstable balancing points. Let P be
a balancing point and let the curvature of the boundary at P be given by k. Show
that if 1/k is greater than the distance from P to the centroid then
P is stable and if 1/k is less than the distance
from P to the centroid then
P is unstable. |
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