Image:Circle epicircle.gif
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[edit] Summary
Description:
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.
Created:
26 July 2006
Author: Cleonis
[edit] Licensing
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This work is licensed under the Creative Commons Attribution-ShareAlike 2.5 License. |
File history
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| Date/Time | Dimensions | User | Comment | |
|---|---|---|---|---|
| current | 09:48, 25 July 2006 | 256×256 (35 KB) | Cleonis (Talk | contribs) | ('''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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