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.