a) Find the unit tangent, T, vector when t = The principal unit normal when t = is N = < 0,0,−1 >. Using this fact find the binormal vector, B, when t = c) Sketch 7, T, Ñ, B when t = (lengths do not need to be exact). Reproduce any of the graphs above in your work (large and detailed) and position your vectors appropriately on your graph.
a) Find the unit tangent, T, vector when t = The principal unit normal when t = is N = < 0,0,−1 >. Using this fact find the binormal vector, B, when t = c) Sketch 7, T, Ñ, B when t = (lengths do not need to be exact). Reproduce any of the graphs above in your work (large and detailed) and position your vectors appropriately on your graph.
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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Question
Transcribed Image Text:a)
b)
Find the unit tangent, T, vector when t =
F..
d)
e)
The principal unit normal when t = is Ñ = < 0,0,−1 >.
Using this fact find the binormal vector, B, when t
=7
c)
Sketch 7,7, Ñ, B when t = (lengths do not need to
be exact). Reproduce any of the graphs above in your work
(large and detailed) and position your vectors appropriately on
your graph.
TL
Find the equation of the osculating plane P when t =
Sketch the osculating plane when t = Reproduce your
work on a new graph showing the plane and the path.
f) If the acceleration vector is a = aTT + a₁Ñ when
expressed in terms of the unit tangent and unit normal
vectors, what can you conclude about the magnitude and
direction its tangential component, a T, when t = based
on the path of particle? Explain.
2
Transcribed Image Text:Given the vector function describing the path of a particle:
r(t) =< t, t, sint > fort >
Several sketches of it below (the red axis is the x-axis, the green axis
is the y-axis, the point A is (,1)) from different angles below:
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