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# maple - Lab#2 Space Curves and Motion Department of...

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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 Introduction Describing motion in space Space curves Seeing the path 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 three-dimensional space, we must specify its position at each moment in time. This is a perfect use for a vector-valued 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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More 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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maple - Lab#2 Space Curves and Motion Department of...

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