dy Va2-x2 with initial condition y(a) = 0. dx -a va2-t2 dt This can be solved by y = J %3D II

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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MATH 252 – TRACTRIX
1) Suppose that you are holding a rope of length a and you are going to walk and drag an object
behind you.
In particular suppose that your initial position is (0,0) and that the object's initial position is
(a, 0) and that you will walk in the direction of the positive y-axis.
We wish to find an equation for the path of the dragged object. Let's only worry about the
upper portion (matching walking in positive y direction)
Tractrix with object initially at b
(4,0)
YOU DO: Suppose the object is at (x, y). Determine the y - coordinate of the puller.
HINT: Set up a right triangle. You know 2 of its measurements.
The pulled object is always going towards the puller. We need that following the slope of the
curve would result in the object meeting the current position of the puller. We also have an
initial condition that y(a)
= 0. These conditions give us a differential equation:
dy
Va²-x²
with initial condition y(a) = 0.
dx
Va2-t2
dt
This can be solved by y =
Transcribed Image Text:MATH 252 – TRACTRIX 1) Suppose that you are holding a rope of length a and you are going to walk and drag an object behind you. In particular suppose that your initial position is (0,0) and that the object's initial position is (a, 0) and that you will walk in the direction of the positive y-axis. We wish to find an equation for the path of the dragged object. Let's only worry about the upper portion (matching walking in positive y direction) Tractrix with object initially at b (4,0) YOU DO: Suppose the object is at (x, y). Determine the y - coordinate of the puller. HINT: Set up a right triangle. You know 2 of its measurements. The pulled object is always going towards the puller. We need that following the slope of the curve would result in the object meeting the current position of the puller. We also have an initial condition that y(a) = 0. These conditions give us a differential equation: dy Va²-x² with initial condition y(a) = 0. dx Va2-t2 dt This can be solved by y =
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