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As in the previous question, let y: R → R³ be a unit speed curve, let T, N, B denote the Frenet frame of y, and K, T the curvature and torsion of y. Suppose (t) #0 for all t, and define ß: R → R³ by It can be shown that the curvature of ß can be written in the form where a, b are integers. B(t) = dy(t) dt (1+r°xb)1/2,

As in the previous question, let y: R → R³ be a unit speed curve, let T, N, B denote the Frenet frame of y, and K, T the curvature and torsion of y. Suppose (t) #0 for all t, and define ß: R → R³ by It can be shown that the curvature of ß can be written in the form where a, b are integers. B(t) = dy(t) dt (1+r°xb)1/2,

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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As in the previous question, let y: R. R³ be a unit speed curve, let T, N, B denote the Frenet frame of y, and K, π the curvature and torsion of y. Suppose (t) #0 for all t, and define ß: R → R³ by It can be shown that the curvature of ß can be written in the form where a, b are integers. Then a = and b = B(t) = = dy(t) dt (1+z@rb)1/2,
Transcribed Image Text:As in the previous question, let y: R. R³ be a unit speed curve, let T, N, B denote the Frenet frame of y, and K, π the curvature and torsion of y. Suppose (t) #0 for all t, and define ß: R → R³ by It can be shown that the curvature of ß can be written in the form where a, b are integers. Then a = and b = B(t) = = dy(t) dt (1+z@rb)1/2,
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