Is it possible that there is a relatively nice analytic expression

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Anonymous
2016-10-01 01:32:45 Post No. 8383231
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Anonymous 2016-10-01 01:32:45 Post No. 8383231 [Report]

Is it possible that there is a relatively nice analytic expression for the curves that limit the linearly rotating line segment of an arbitrary length, that translates along a line?
I hope you understand what I'm asking by looking at the picture.

What about the area under the curves? And the volume traced by circles rotating linearly while translating along a line in 3-space, in place of the line segments. (radius is half the length of the segment)
I guess this is very related to the legendary Mario curve of /sci/.

Anonymous 2016-10-01 01:38:25 Post No.8383245
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Anonymous 2016-10-01 01:38:25 Post No.8383245 [Report]

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Here's the circles.

Anonymous 2016-10-01 02:03:16 Post No.8383274
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Anonymous 2016-10-01 02:03:16 Post No.8383274 [Report]

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am interested.
bump

Anonymous 2016-10-01 02:12:15 Post No.8383285
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Anonymous 2016-10-01 02:12:15 Post No.8383285 [Report]

ummmm... sine?

A rotating stationary diameter traces out two simultaneous and opposite radii.
If the lateral translation was constant and parametrized by time, the curve would simply be sin xt.

Anonymous 2016-10-01 02:16:36 Post No.8383289
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Anonymous 2016-10-01 02:16:36 Post No.8383289 [Report]

>>8383285
I believe this anon has it right. If you were to continue your drawing in the first picture, you should develop something that looks like a sine graph.

Anonymous 2016-10-01 02:27:51 Post No.8383303
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Anonymous 2016-10-01 02:27:51 Post No.8383303 [Report]

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>>8383231
Curtate cycloid. Pic related. To encourage you to derive the equations yourself, the link to mathematica page on curtate cycloids has been omitted

Anonymous 2016-10-01 02:33:47 Post No.8383313
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Anonymous 2016-10-01 02:33:47 Post No.8383313 [Report]

>>8383303
I'm not OP, but that "rod" isn't moving in a straight line with constant velocity. If you look at OP's pic, the center of mass of the rod is always on that line.

Anonymous 2016-10-01 02:43:15 Post No.8383322
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Anonymous 2016-10-01 02:43:15 Post No.8383322 [Report]

>>8383313

anon's picture tracks the motion of one end at a time. The other half of the is going to be the same curve 1 pi out of phase.

Anonymous 2016-10-01 02:49:44 Post No.8383333
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Anonymous 2016-10-01 02:49:44 Post No.8383333 [Report]

>>8383274
Why are you using the spider?

Anonymous 2016-10-01 03:04:12 Post No.8383350
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Anonymous 2016-10-01 03:04:12 Post No.8383350 [Report]

>>8383303
>curtate cycloid
How come it's not just a cycloid?

Anonymous 2016-10-01 03:05:21 Post No.8383351
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Anonymous 2016-10-01 03:05:21 Post No.8383351 [Report]

>>8383322
sorr,y this isn't exactly right. but if the y position of the end of the rod with y equaling 0 on the line one end of the rod would be traced with sinx and the other end of the rod would be traced with sin x-pi/2 aka cosine x.

Anonymous 2016-10-01 13:16:23 Post No.8383941
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Anonymous 2016-10-01 13:16:23 Post No.8383941 [Report]

Isn't it just an ordinary cycloid, which can't have an expression of the form y=f(x)?

Anonymous 2016-10-01 16:56:34 Post No.8384230
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Anonymous 2016-10-01 16:56:34 Post No.8384230 [Report]

Actually doesn't this differ from a cycloid in that the rotating segment translates an arbitrary distance during a full cycle, while with the cycloid it's always 2*pi*r?
Is there a name for this or am I too stupid to see that it's actually some type of cycloid?

Anonymous 2016-10-02 02:01:05 Post No.8385258
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Anonymous 2016-10-02 02:01:05 Post No.8385258 [Report]

>>8383231
Is rotation in the same plane as the translation or not?

I'm aware that Imgur.com will stop allowing adult images since 15th of May. I'm taking actions to backup as much data as possible. Read more on this topic here - https://archived.moe/talk/thread/1694/

I'm aware that Imgur.com will stop allowing adult images since 15th of May. I'm taking actions to backup as much data as possible.
Read more on this topic here - https://archived.moe/talk/thread/1694/