(A clothoid curve) The plane curve C in Figure 11.28 has par
Question and Solution
(A clothoid curve) The plane curve C in Figure 11.28 has parametric equations x.s/ D Z s 0 cos kt2 2 dt and y.s/ D Z s 0
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(A clothoid curve) The plane curve C in Figure 11.28 has parametric equations x.s/ D Z s 0 cos kt2 2 dt and y.s/ D Z s 0 sin kt2 2 dt: Verify that s is, in fact, the arc length along C measured from .0; 0/ and that the curvature of C is given by .s/ D ks. Because the curvature changes linearly with distance along the curve, such curves, called clothoids, are useful for joining track sections of different curvatures.
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