Find a change of parameter t = g(τ ) for the parabolic arc r(t) = t^2i + tj, −1 ≤ t ≤ 1 such that the arc is traced from the point (1, 1) to (1, −1) as τ varies over the interval [0, 4].
Find a change of parameter t = g(τ ) for the parabolic arc r(t) = t^2i + tj, −1 ≤ t ≤ 1 such that the arc is traced from the point (1, 1) to (1, −1) as τ varies over the interval [0, 4].
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
Find a change of parameter t = g(τ ) for the parabolic arc
r(t) = t^2i + tj, −1 ≤ t ≤ 1
such that the arc is traced from the point (1, 1) to (1, −1) as τ varies over the interval [0, 4].
Expert Solution
Step 1
Change of transformation must be a continuous function, there are so many parametrization, we use simple the linear polynomial,
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