Manuals/calci/LISSAJOUS

LISSAJOUS (TypeOrSettings,AsTable)

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle TypeOrSettings} is any type like Ellipse or circle and so on.

Description

• This function shows the values of the Lissajous curve.
• 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: In the Lissajous equation,a=1,b=1,A=1,B=1 and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \delta} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{\pi}{2}} radians, the figure is a circle.
• So these values substitute in the equation and it will shows the result.With the above values when $\delta$=0,then the value will show for line.
• In the same way the ratio Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{a}{b}} =1 and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \delta} =0,then the values will be shown for ellipse.
• Suppose Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{a}{b}} = 2, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \delta} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{\pi}{4}} , then the values will show for parabola.
• The Lissajous curve gets more complicated for other ratios, which are closed only if a/b is rational.

See Also

• FRACTAL
• LISSAJOUSCURVE

References

• Lissajous

• List of Main Z Functions

• Z3 home