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September 17, 2025, 11:48:03 am
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Author Topic: Smoothness in parametric equations  (Read 1098 times)  Share 

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  • Victorian
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Smoothness in parametric equations
« on: February 18, 2010, 05:17:16 pm »
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Is there a test of some kind to determine whether a parametric equation is smooth?

Say you have a parametric equation such as

So , and obviously the derivative is defined for all t.

However, if you graph you will get cusps at




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TrueTears

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Re: Smoothness in parametric equations
« Reply #1 on: February 18, 2010, 05:20:51 pm »
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For r(t) to be smooth r'(t) must be continuous and never equal to the 0 vector.

But r'(t) = 0 when t = npi/2

It is explained in Stewarts pg 831 on the bottom.
« Last Edit: February 18, 2010, 05:23:46 pm by TrueTears »
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PhD @ MIT (Economics).

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  • Victorian
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Re: Smoothness in parametric equations
« Reply #2 on: February 18, 2010, 05:27:26 pm »
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ah thanks TT, didn't know that
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