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(d) The Frenet-Serret equations are given by dT ི||ž「ལྦ KN -KT+TB -TN Using these equations, prove the following identities. (i) r" = s"T+ (s')²KN (ii) r′ × r″ = (s')³kB As a hint, start with the result from the lectures that r' =s'T and also that N=BxT.

(d) The Frenet-Serret equations are given by dT ི||ž「ལྦ KN -KT+TB -TN Using these equations, prove the following identities. (i) r" = s"T+ (s')²KN (ii) r′ × r″ = (s')³kB As a hint, start with the result from the lectures that r' =s'T and also that N=BxT.

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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(d) The Frenet-Serret equations are given by dT ི||ž「ལྦ KN -KT+TB -TN Using these equations, prove the following identities. (i) r" = s"T+ (s')²KN (ii) r′ × r″ = (s')³kB As a hint, start with the result from the lectures that r' =s'T and also that N=BxT.
Transcribed Image Text:(d) The Frenet-Serret equations are given by dT ི||ž「ལྦ KN -KT+TB -TN Using these equations, prove the following identities. (i) r" = s"T+ (s')²KN (ii) r′ × r″ = (s')³kB As a hint, start with the result from the lectures that r' =s'T and also that N=BxT.
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