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File:Circle epicircle.gif

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Circle_epicircle.gif (256 × 256 pixels, file size: 35 KB, MIME type: image/gif, looped, 60 frames, 6.0 s)

Summary

Description
English: The following parametric equation describes the motion of the dot that follows the ellips-shaped line:

x = a*cos(wt)
y = b*sin(wt)
That parametric equation can be regrouped, with c = (a+b)/2 and d = (a-b)/2
That gives:
x = c*cos(wt) + d*cos(wt)
y = c*sin(wt) - d*sin(wt)

The animation illustrates that the motion along the ellipse-shaped trajectory can be seen as a vector combination of motion along a circle (here counter-clockwise), and motion along an epi-circle (here clockwise). If the motion is transformed to motion with respect to a rotating coordinate system (with the rotating coordinate system co-rotating with the main circle), then only the motion along the epi-circle remains.
Date
Source Own work; Diagram created by uploader
Author Cleonis (talk) (Uploads)

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26 July 2006

image/gif

8fdc545187efe0148bd187aa388dda40eea27f45

36,048 byte

5.999999999999995 second

256 pixel

256 pixel

File history

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Date/TimeThumbnailDimensionsUserComment
current09:48, 25 July 2006Thumbnail for version as of 09:48, 25 July 2006256 × 256 (35 KB)Cleonis'''Description:'''<br> The following parametric equation describes the motion of the dot that follows the ellips-shaped line x = a*cos(wt) y = b*sin(wt) That parametric equation can be regrouped, with c = (a+b)/2 and d = (a-b)/2 That g

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