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.
to share – to copy, distribute and transmit the work
to remix – to adapt the work
Under the following conditions:
attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
'''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