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2. The Cornu (or Euler) spiral, shown below, is defined by t πυζ (S²) (['coe (²) du. ["rin (#²) de) du). COS 2 0 It is used in road design, to create a gradual transition from a straight road to a constant curvature ramp. (a) Show that the parameter t is an arc length parametrisation. (b) Show that the curvature K = π|t|.

2. The Cornu (or Euler) spiral, shown below, is defined by t πυζ (S²) (['coe (²) du. ["rin (#²) de) du). COS 2 0 It is used in road design, to create a gradual transition from a straight road to a constant curvature ramp. (a) Show that the parameter t is an arc length parametrisation. (b) Show that the curvature K = π|t|.

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 ot ([cos (²) ds. COS du, 0 •t 4. ["* sin (T2²) du). It is used in road design, to create a gradual transition from a straight road to a constant curvature ramp. (a) Show that the parameter t is an arc length parametrisation. (b) Show that the curvature K = π|t|.
Transcribed Image Text:2. The Cornu (or Euler) spiral, shown below, is defined by ot ([cos (²) ds. COS du, 0 •t 4. ["* sin (T2²) du). It is used in road design, to create a gradual transition from a straight road to a constant curvature ramp. (a) Show that the parameter t is an arc length parametrisation. (b) Show that the curvature K = π|t|.
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