Manuals/calci/LISSAJOUSCURVE

LISSAJOUSCURVE (Type,Div,Settings)

Description

This function shows the Lissajous curve for each values.
Lissajous Curve is a parametric plot of the harmonic system.
It is also called Bowditch Curves.Lissajous used sounds of different frequencies to vibrate a mirror.
A beam of light reflected from the mirror, was allowed to trace patterns which depended on the frequencies of the sounds – in a setup similar to projectors used in today's laser light shows.
Lissajous figure is the intersection of two sinusoidal curves, the axes of which are at right angles to each other.
Mathematically, this translates to a Complex harmonic function:

$x=ASin(at+\delta )$ , $y=BSin(bt)$

The appearance of a figure is highly sensitive to a/b, the ratio of a and b.
According to the ratio value, the shapes of the figures change in interesting ways.
For a a/b ratio=1, the figure is an ellipse.
For a=b, $\delta$ = ${\frac {\pi }{2}}$ radians, the figure is a circle.
For $\delta$ = 0, the figure is a line.
For a/b = 2, $\delta$ = ${\frac {\pi }{4}}$ , the result is a parabola.
The Lissajous curve gets more complicated for other ratios, which are closed only if a/b is rational.