# Lissajous curve

In the classical oscilloscopic representation, a physical quantity is represented in a time reference. It is different with the Lissajous figures. Here the X-axis of the oscilloscope is deflected by a sinusoidal voltage

. In Lissajous figures, the vertical and horizontal deflections are controlled by synchronous sinusoidal signals. The resulting displays show intertwined figures from which phase shifts

and harmonic relationships can be determined.

If both deflections, the horizontal and the vertical, are performed with the same frequency and phase position, a diagonal line appears on thescreen

as a Lissajous figure.

As the phase between the two frequencies changes, the line opens and an ellipse appears, which becomes a circle at a phase difference of 90°.

The Lissajous figures are named after their discoverer, the French mathematician Jules Antoine Lissajous (1822 to 1180).