Consider a plane curve defined by the parametric equations : x(t)=acos^3 (t) and y(t)=asin^3 (t) where a is a constant and 0≤t≤2π. This curve is known as the astroid. Find the curvature κ(t) of this curve at any point t. Specifically, calculate the curvature at t= π/4 .
Consider a plane curve defined by the parametric equations : x(t)=acos^3 (t) and y(t)=asin^3 (t) where a is a constant and 0≤t≤2π. This curve is known as the astroid. Find the curvature κ(t) of this curve at any point t. Specifically, calculate the curvature at t= π/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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Consider a plane curve defined by the parametric equations :
x(t)=acos^3 (t) and y(t)=asin^3 (t)
where a is a constant and 0≤t≤2π.
This curve is known as the astroid.
Find the curvature κ(t) of this curve at any point t.
Specifically, calculate the curvature at t= π/4 .
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