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2. The Cornu (or Euler) spiral, shown below, is defined by r(s) = (f* cos (u²) du, f *cos (u²) du, ["* sin (u²) du). It is used in road design, to create a gradual transition from a straight road to a constant curvature ramp. X (a) Show that the parameter s is arc length parametrisation by computing dr/ds.

2. The Cornu (or Euler) spiral, shown below, is defined by r(s) = (f* cos (u²) du, f *cos (u²) du, ["* sin (u²) du). It is used in road design, to create a gradual transition from a straight road to a constant curvature ramp. X (a) Show that the parameter s is arc length parametrisation by computing dr/ds.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. The Cornu (or Euler) spiral, shown below, is defined by r(s) = =(√² cos *cos (u²) (u²) du, ["* sin (u²) du). It is used in road design, to create a gradual transition from a straight road to a constant curvature ramp. X (a) Show that the parameter s is arc length parametrisation by computing dr/ds. (b) Show that the curvature K = 2|s|.
Transcribed Image Text:2. The Cornu (or Euler) spiral, shown below, is defined by r(s) = =(√² cos *cos (u²) (u²) du, ["* sin (u²) du). It is used in road design, to create a gradual transition from a straight road to a constant curvature ramp. X (a) Show that the parameter s is arc length parametrisation by computing dr/ds. (b) Show that the curvature K = 2|s|.
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