A curve is given parametrically by r(t) = f(t) i + g(t) j. Show that, if s
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A curve is given parametrically by r(t) = f(t) i + g(t) j. Show that, if s is the length of an arc measured from a fixed point P0 on the curve so that s increases as t increases, then
Deduce that dr/ds is a unit tangent vector to the curve at r(t) and that dr/ds and d2r/ds2 are perpendicular. Show that
where κ is the curvature of the curve at that point.
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