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May 12th, 2012, 11:50 AM   #1
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What curve is this?

Hello!

Can somebody tell me what curve is this:

(at; b sint; c cost), t e R
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May 12th, 2012, 11:57 AM   #2
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Re: What curve is this?

I believe it is an elliptical helix.
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May 25th, 2012, 01:35 PM   #3
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Re: What curve is this?

Can someone plot this curve in http://www.wolframalpha.com/, or some other program?
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May 25th, 2012, 02:42 PM   #4
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For what values of a, b and c?
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May 26th, 2012, 12:27 AM   #5
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Re:

Quote:
Originally Posted by skipjack
For what values of a, b and c?
It dont says, just that t e R.. I guess that a,b,c are from Z, or R
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May 26th, 2012, 12:35 AM   #6
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Re: What curve is this?

In order to plot a unique member of the family of curves given by the original parametric equations you have to choose values for a, b, and c.

Suppose we choose a = 1, b = 2 and c = 3, where 0 < t < 2?. To plot the curve in W|A, use the command:

plot x=t, y=2*sin(t), z=3*cos(t) for 0<t<2*pi

to get:

[attachment=0:3abg6ouj]ellipticalhelix.jpg[/attachment:3abg6ouj]
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File Type: jpg ellipticalhelix.jpg (19.4 KB, 135 views)
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May 26th, 2012, 12:45 AM   #7
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Re: What curve is this?

Thank you. What wolud be equation of this curve without parameter t?
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May 26th, 2012, 01:13 AM   #8
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Re: What curve is this?

You would have two equations by eliminating the parameter, but it is most often that a 3-space curve such as a helix is represented parametrically I believe.
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May 26th, 2012, 01:53 AM   #9
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Re: What curve is this?

Quote:
Originally Posted by MarkFL
You would have two equations by eliminating the parameter, but it is most often that a 3-space curve such as a helix is represented parametrically I believe.

what are flexion and torsion? Are they constant?
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