Lab #2: Space Curves and Motion
Department of Mathematics, Statistics, and Computer Science
University of Illinois at Chicago
by Paul Brown, Heidi Burgiel, Marc Culler
Copyright © 1999, The University of Illinois at Chicago
Maple is a registered trademark of Waterloo Maple Software
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Introduction
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Describing motion in space
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Space curves
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Seeing the path
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Lab Assignment # 2
Introduction
In this short lab project, you will use Maple to visualize space curves, motion in space,
and to understand the difference between a space curve and a position function .
Describing motion in space
To describe the motion of a particle moving in threedimensional space, we must specify
its position at each moment in time. This is a perfect use for a vectorvalued function ,
i.e., a function of the form
where x , y , and z are all functions of t. We think of the variable t as "time" and of the
vector P(t) as the "position at time t". We could visualize this vector as an arrow starting
at the origin and ending at the point ( x (t), y (t), z (t)) where the particle lies at time t, but
we usually just think of the point and ignore the vector. When used to describe the
motion of a particle in space, a vector valued function is called a position function .
Space curves
Imagine now that our moving particle leaves a trail in space, something like the vapor
trail left by a jet airplane. This trail is what we call the space curve parameterized by the
vector valued function P (t). The variable t is a parameter , so this is simply a way of
saying that the function P (t) is a way of describing the space curve as it elapses in time.
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View Full DocumentMore concretely, your signature on a piece of paper is a space curve, but the position of
the point of the pen as a function of time is a position function.
Let's get started using Maple:
Open a Maple worksheet.
Type:
>
with(plots);
The output from this command is a list of all of the special graphics commands contained
in the "plots" package. When you start Maple, it loads only a small collection of general
purpose commands (such as those we used last week). This helps to conserve memory
and allows you to load just the commands you plan to use. If you would rather not see the
list of plot commands, then you can use a colon instead of a semicolon at the end of the
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 Spring '10
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 Math, Statistics, Vectorvalued function, space curve, Waterloo Maple

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