Nina del Ser - Mathematics
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(2) shows that the curve will preserve its elliptic character, irrespective of the value given to b, as long as b
1. When b 0, it is clear that (2) generates a unit circle (which is therefore simply a special case of the ellipse,
in which the two foci lie on top of each other), centered at the origin. Figure 4 shows what happens when the
lengths of the primary and secondary rotors are identical (i.e. b 1):
Since the y-component of the position vector of the seat is always equal to zero, the seat will only move along
the x-axis.
figure 4
Thus, if the lengths of the primary and secondary rotors were equivalent, people would just travel back and
forth in a straight line, which might be of some relief to nervous passengers!
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