I got interested in making nice pictures in Mathematica again, after a hiatus of ~5 years. I suppose I should be writing up on how I generated these samples, but I’ll try to formalize the mathematics behind these first. For now, enjoy these short movies!

\Jan

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Hi Simon! It’s actually a rolling parabola. The focus of a rolling parabola traces out a catenary, the curve a chain or string hanging from two points makes. I have working code, but explaining how to do it is a bit difficult. I suppose I should write about it in a future entry.

I am Chandru1 from stackexchange. I see that you have drawn wonderful diagrams. I would like to have this diagram worked out for me. I don’t know how to draw pics.

Could you please draw the graph of the curve when is even and tell me what happens when .

The rolling curve is a parabola, while the curve being traced out is a catenary. I have a derivation written, but the words to explain what I did so the rest of you can understand are proving to be hard to write. :)

Neat! There was an article this year in the College Mathematics Journal called “The locus of the focus of a rolling parabola” that you might find interesting.

Very pretty! A quick search (http://demonstrations.wolfram.com/search.html?query=cycloid) shows that there is no demonstration of a rolling hyperbola, maybe you should make one?

Hi Simon! It’s actually a rolling parabola. The focus of a rolling parabola traces out a catenary, the curve a chain or string hanging from two points makes. I have working code, but explaining how to do it is a bit difficult. I suppose I should write about it in a future entry.

Respected J.M,

I am Chandru1 from stackexchange. I see that you have drawn wonderful diagrams. I would like to have this diagram worked out for me. I don’t know how to draw pics.

Could you please draw the graph of the curve when is even and tell me what happens when .

Hello Chandru, I suggest researching on the so-called LamÃ© curves; some looking around gives me websites that have pretty pictures of these, probably better than what I can hope to create. :)

Lovely graphics. I particularly liked the first one. Seems that the red trajectory is a parabola as well as the blue one.

The rolling curve is a parabola, while the curve being traced out is a catenary. I have a derivation written, but the words to explain what I did so the rest of you can understand are proving to be hard to write. :)

Ok, no problem. The visual result will do. :-)

Keep up the good work!

Neat! There was an article this year in the College Mathematics Journal called “The locus of the focus of a rolling parabola” that you might find interesting.

http://www.jstor.org/stable/10.4169/07468342.41.2.129

Looks pretty neat!

I have a similar post and I have included code that works for the prolate and curtate cycloids.

here is the link

http://blog.isallaboutmath.com/2008/01/19/producing-animations-with-mathematica-60-is-as-easy-as-pie/