Finding planar curves with constant curvature

Sep 2012
106
22
United States
Hey guys,

I'm completely stuck on the following question:

Find all planar curves with constant curvature

When K = 0, it is simply a line. That is easily shown by equating r'(t) = r'(0) and integrating both sides. This is not applicable when curvature is non-zero.
 

chiro

MHF Helper
Sep 2012
6,608
1,263
Australia
Hey ShadowKnight8702.

Wouldn't something with a constant curvature be a circle?
 
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Sep 2012
106
22
United States
Yeah. As well as a line. I ended up proving this using a moving frame of N, T.