Let P be a point at a distance d from the center of a circle of radius r. The curve traced out by P as the circle rolls along a straight line is called a trochoid. (Think of the motion of a point on a spoke of a bicycle wheel.) The cycloid is the special case of a trochoid with d = r. Using the same parameter θ as for the cycloid and, assuming the line is the x-axis and θ = 0 when P is at one of its lowest points, parametric equations of the trochoid are x = rθ − d sin(θ) y = r − d cos(θ). Find the area under one arch of the trochoid found above for the case d < r.
Let P be a point at a distance d from the center of a circle of radius r. The curve traced out by P as the circle rolls along a straight line is called a trochoid. (Think of the motion of a point on a spoke of a bicycle wheel.) The cycloid is the special case of a trochoid with d = r. Using the same parameter θ as for the cycloid and, assuming the line is the x-axis and θ = 0 when P is at one of its lowest points, parametric equations of the trochoid are x = rθ − d sin(θ) y = r − d cos(θ). Find the area under one arch of the trochoid found above for the case d < r.
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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Let P be a point at a distance d from the center of a circle of radius r. The curve traced out by P as the circle rolls along a straight line is called a trochoid. (Think of the motion of a point on a spoke of a bicycle wheel.) The cycloid is the special case of a trochoid with d = r.
Using the same parameter θ as for the cycloid and, assuming the line is the x-axis and θ = 0 when P is at one of its lowest points, parametric equations of the trochoid are
x = rθ − d sin(θ) y = r − d cos(θ).
Find the area under one arch of the trochoid found above for the case d < r.
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