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61. (a) Show that dB/ds is perpendicular to B. (b) Show that dB/ds is perpendicular to T. (c) Deduce from parts (a) and (b) that dB/ds-T(S)N for some number 7(s) called the torsion of the curve. (The torsion measures the degree of twisting of a curve.) (d) Show that for a plane curve the torsion is 7(s) = 0.

61. (a) Show that dB/ds is perpendicular to B. (b) Show that dB/ds is perpendicular to T. (c) Deduce from parts (a) and (b) that dB/ds-T(S)N for some number 7(s) called the torsion of the curve. (The torsion measures the degree of twisting of a curve.) (d) Show that for a plane curve the torsion is 7(s) = 0.

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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61. (a) Show that dB/ds is perpendicular to B. (b) Show that dB/ds is perpendicular to T. (c) Deduce from parts (a) and (b) that dB/ds = T(S)N for some number 7(s) called the torsion of the curve. (The torsion measures the degree of twisting of a curve.) (d) Show that for a plane curve the torsion is 7(s) = 0.
Transcribed Image Text:61. (a) Show that dB/ds is perpendicular to B. (b) Show that dB/ds is perpendicular to T. (c) Deduce from parts (a) and (b) that dB/ds = T(S)N for some number 7(s) called the torsion of the curve. (The torsion measures the degree of twisting of a curve.) (d) Show that for a plane curve the torsion is 7(s) = 0.
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