Lissajous curve

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A Lissajous curve , also known as Lissajous figure or Bowditch curve , is the graph of a system of parametric equations x = A sin ⁡ ( a t + δ ) , y = B sin ⁡ ( b t ) , {\displaystyle x=A\sin(at+\delta ),\quad y=B\sin(bt),} which describe the superposition of two perpendicular oscillations in x and y directions of different angular frequency (a and b). The resulting family of curves was investigated by Nathaniel Bowditch in 1815, and later in more detail in 1857 by Jules Antoine Lissajous (for whom it has been named). Such motions may be considered as a particular kind of complex harmonic motion. The appearance of the figure is sensitive to the ratio ⁠a/b⁠. For a ratio of 1, when the frequencies match a=b, the figure is an ellipse, with special cases including circles...

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