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The function
is differentiable more tna twice over
. We have:
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|
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The tangent to the graph at
has equation
, and the normal
at
has equation
. The center of curvature is the point
on
at a distance of
from
and ``inside'' the curve; thus the coordinates of
are
.
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The curvature at
is given by the formula:
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Physicists use to denote
instead of
and
instead of
; the above formula becomes:
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The curve is an ellipse, whose cartesian equation is
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We use the formula in Proposition 13.4. We have:
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We compute these derivatives for
; we have:
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(6.2) |
Noah Dana-Picard 2007-12-28