1) Consider the spiral r:-7, 7 R' defined by (cos(s) r(s) sin(s). i) Compute the unit tangent vector t(s) – r'(s)/|P(s)| ii) Compute the normal n(s) ii) Compute b(s) = t(s) × n(s). iv) State the Cartesian equation of the plane which passes throu r(s) and has normal b(s) (this is called the "oseulating plane" which literally means the plane that kisses the eurve, so called because this plane has maximum contact with the curve). v) The coeflicient 7 such that b'(s) curve (geometrically, this coeflicient measures how the eurve twists throngh space). State the torsion of the spiral. ) For a general curve r: / R, define the vectors t(s), n(s) and b(s) as l'(s)/||t(s)||- TH(s) is called the torsion of the t'(s) t(s) ,n(s) and b(s) t(s) x n(s), You may assume r'(s)|| and ||t'(N)|| are non
1) Consider the spiral r:-7, 7 R' defined by (cos(s) r(s) sin(s). i) Compute the unit tangent vector t(s) – r'(s)/|P(s)| ii) Compute the normal n(s) ii) Compute b(s) = t(s) × n(s). iv) State the Cartesian equation of the plane which passes throu r(s) and has normal b(s) (this is called the "oseulating plane" which literally means the plane that kisses the eurve, so called because this plane has maximum contact with the curve). v) The coeflicient 7 such that b'(s) curve (geometrically, this coeflicient measures how the eurve twists throngh space). State the torsion of the spiral. ) For a general curve r: / R, define the vectors t(s), n(s) and b(s) as l'(s)/||t(s)||- TH(s) is called the torsion of the t'(s) t(s) ,n(s) and b(s) t(s) x n(s), You may assume r'(s)|| and ||t'(N)|| are non
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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Needed to be solved part IV,V and VI correctly in 10 minutes and get the thumbs up please show neat and clean work
Transcribed Image Text:) Consider the spiral r: (-x, 7|R' defined by
r(s)
xin(s)
i) Compute the unit tangent vector t(s)= r(s)/||r'(s)||-
ii) Compute the normal n(s)
iii) Compute b(s) = t(s) x n(s).
iv) State the Cartesian equation of the plane which passes throu r(s) and
has normal b(s) (this is called the "osculating plane" which literally means
the plane that kisses the eurve, so called because this plane has maximum
contact with the curve).
v) The coefficient 7 such that b'(s)
curve (geometrically, this coeflicient measures how the curve twists throngh
space). State the torsion of the spiral.
t'(s)/||t'()||.
Tu(s) is called the forsion of the
) For a general curve r:/→R, define the vectors t(s), n(s) nd b(s) as
t(s)
n(s)
t'(s)
and b(s)
t(s) × n(s),
may assume r(s)|| and || || are non zero.
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