Manuals/calci/LISSAJOUS
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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 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 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.
Examples
- LISSAJOUS("circle",4..6)
| 4.999998731727338 | 1 |
| 4.98033339924072 | 1.3993336665873126 |
| 4.9208978911521815 | 1.7946773231802449 |
| 4.822286067411776 | 2.1820808266453584 |
| 4.685483224765582 | 2.5576733692346023 |
| 4.511856251996312 | 2.917702154416812 |
| 4.303139972422432 | 3.2585698935801415 |
| 4.061419810117014 | 3.576870748950764 |
| 3.789110953039751 | 3.8694243635980907 |
| 3.48893422127722 | 4.133307638509933 |
| 3.163888881507954 | 4.365883939231585 |
| 2.817222679321226 | 4.564829440245742 |
| 2.4523993888166733 | 4.728156343868905 |
| 2.073064203718472 | 4.854232741668772 |
and so on.
Related Videos
See Also
References