Lissajous figures article about lissajous figures by the. This property is exploited to produce a set of points, called padua points, at which a function may be sampled in order to compute either a bivariate interpolation or quadrature of the function over the domain. Project muse drawings based on laser lissajous figures. Lissajous figure, also called bowditch curve, pattern produced by the intersection of two sinusoidal curves the axes of which are at right angles to each other.
Given two wheels connected by a belt and a point on the outer rim of each, one can generate a lissajous figure by the motion of the wheels. If the ratio of the two frequencies of the voltages is just equal to a rational number, standing figures appear on the oscilloscope. Download the citation and abstract in bibtex format download the citation and abstract in. Lissajous figures by jed margolin in the old days, whenever they showed an engineer working, there was usually an oscilloscope nearby with a pattern on the screen. This tutorial is a threedimensional simulation of a cathode ray oscilloscope producing lissajous figures as it compares sinusoidal voltages. The very heavy piece of castiron apparatus at the right sits in my living room, where it menaces the unwary toe. Lissajous figures are produced in two dimensions when the x and y coordinates are given by two sine waves, which may have any amplitude, frequency and phase. The aim of this experiment is to show how to trace the lissajous figures on the cathode ray oscilloscope using two function generators connected to. Jules lissajous and his figures j ules antoine lissajous 18221880 is not among the giants in the history of science, yet his name is known to physics students through the lissajous.
Lissajous figures, displaying vi curves, or the phase difference between two waveforms. How to draw 2d oscillations and lissajous curves using 3d. In chapter 5, a twodimensional scatter graph is used to plot lissajous figures. Lissajous figures by kitwallace is licensed under the creative commons attribution share alike license. In lieu of an abstract, here is a brief excerpt of the content leonardo, vol. Lissajous figure definition of lissajous figure by the. If the oscilloscope hasthe xversusy capability, one can apply one signal to the vertical deflection plates whileapplying a second signal to the horizontal deflection plates. Each cycle object is independent with controls for frequency, phase and amplitude. The lissajous pattern or lissajous figure is named for the french mathematician jules antoine lissajous 1. Lissajous patterns of cro or cathode ray oscilloscope. This paper proposes an analytical tool with graphical repre sentation based on lissajous curves to analyze the energy or power flow at the. Then the curve reverses direction to retrace its path. The values of a and b have a particularly strong effect on the shape of the curve a determines the number of horizontally aligned lobes and b determines the number of.
Pdf discrete lissajous figures and applications researchgate. Polarization 515 5rt4 it 3rt4 rt4 31t4 57t4 3rt2 71t4 27t 114 712 fig. The coordinates of a point on a wheel can be described by sine functions of a certain frequency and phase shift. Lissajou figures click on the sketch to change the x and y frequencies or wait a while, and theyll change at random lissajous figures openprocessing sketch. The diagram shown is identical to one of the figures you can obtain with the laser lissajous device. Circuits and electronics laboratory a lissajous leesuhzhoo. It explores the field of harmony and disorder and let the user dip into an elegant, dreamlike. Such figures are widely used in frequency and phase measurements see illustration. Lissajouslike figures with triangular and square waves. Jules antoine lissajous 18221880 was a french physicist who.
In figure 1, the curve appears to have a start point and an end point end. When both pairs of the deflection plates horizontal deflection plates and vertical deflection plates of cro cathode ray oscilloscope are connected to two sinusoidal voltages, the patterns appear at cro screen are called the lissajous pattern. Phy2028 practical electronics ii information lissajous figures 1 lissajous figures introduction lissajous figures displayed on an oscilloscope can be used to give a quick estimate of the relative phase of two signals at the same frequency. All structured data from the file and property namespaces is available under the creative commons cc0 license. Rms voltage for sine and square waves, and why your dmm might not work right. But these points are actually where the curve velocity goes to zero. Using your code to investigate lissajous figures and beats, as described below. Lissajous figures plane curves traced by a point which executes two independent harmonic motions in perpendicular directions, the frequencies of the motion being in the ratio of two integers. The sinusoidal output from a wave generator, g, is input simultaneously into a tweeter, t, and. Liassajou curves are described by the parametric equations below. Geometrical and graphical representations analysis of lissajous figures in rotor dynamic system hisham a. A lissajous figure is produced by taking two sine waves and. Introduction lissajous figures displayed on an oscilloscope can be used to give a quick estimate of the relative phase of two signals at the same frequency. Permission is granted to copy, distribute andor modify this document under the terms of the gnu free documentation license, version 1.
These 3d lissajous figures are parametric curves, where each of xt, yt, and zt is a sine function. Lissajous figure definition is any of an infinite variety of curves formed by combining two mutually perpendicular simple harmonic motions, commonly exhibited by the oscilloscope, and used in studying frequency, amplitude, and phase relations of harmonic variables. Let us compute the period of this curve, assuming that. First studied by the american mathematician nathaniel bowditch in 1815, the curves were investigated independently by the french. This page can be used as a playground or learning tool to see how changing basic parameters affects the generated images. Both tuning forks can be driven, allowing steadystate lissajous figures to be displayed. Pdf in this paper, an innovative method based on an algorithm utilizing discrete convolutions of discretetime functions is developed to obtain. Lissajous figure synonyms, lissajous figure pronunciation, lissajous figure translation, english dictionary definition of lissajous figure. Geometrical and graphical representations analysis of. Lissajous a simple example of 2d line plot in matlab, and creating a gui without guide. At the back is a device once used to hold a light source, and a previous owner has mounted a lens on the base of the device. This is a short simple bootable program that animates some lissajous figures.
Before the days of digital frequency meters and phase locked loops, lissajous figures were used to determine the frequencies of sounds or radio signals. One may argue, on such basis, that it is a straightforward mathematical procedure to outguess the lissajouslike figures reported here and computer simulations are needless. A beam of light reflected from the mirror would trace patterns which depended. A signal of known frequency was applied to the horizontal axis of an oscilloscope, and the signal to be measured was applied to the vertical axis. To use lissajous figures to take phase measurements. Use a laser pointer and two small rotating mirrors to create a variety of lissajous figures.
Lissajous is a complex audiovideo signal generator built in maxmsp and inspired by the work of jules antoine lissajous. Or it can be used to create and save your own lissajous artwork. Depending on these parameters, the resulting shape may or. Generating lissajous figures wolfram demonstrations project. A lissajous curve, named after jules antoine lissajous is a graph of the following two parametric equations. Lissajous art peter elsea 112608 2 figure 1 is a basic lissajous generator.
One advantage of eps figures is the ability to use the psfrag package to replace axis labels etc. See harmonic motion typical lissajous figures for ratios of vertical frequency. Hence, apply the sinusoidal signals, which have same amplitude and frequency to both horizontal and vertical deflection plates of cro. Lissajous figures are a special case of parametric equations, where x and y are in the following form. Lissajous curve methods for the identification of nonlinear circuits. Lissajous figures are patterns generated by the junction of a pair of sinusoidal waves with axes that are perpendicular to one another. The user interface above allows you to modify each of these five parameters and see how the graph is affected. Lissajous figures in the application of microvibration.
Frequency measurements using lissajous figures lissajous pattern also helps to. Lissajous figures lissajous pronounced leesuhzhoo figures were discovered by the french physicist jules antoine lissajous. Although one can use lissajous figures to fourier analyze a given signal 17 the other way around use fourier analysis to forecast lissajouslike figures is not as easy. Lissajous figures are obtained with an oscilloscope when this is operated in xy mode and when in both channel 1 and 2 voltages are applied. We see another example of parametric equations later in the applications of differentiation section. A copy of the license is included in the section entitled gnu free documentation license. Lissajous figures a lissajous figure is produced by taking two sine waves and displaying them at rightangles to each other. Lissajous work in the nineteenth century centered around the study of vibrating objects and wave phenomena. Lissajous figures are generated when the periodic frequency of the x coordinate and the periodic frequency of the y coordinate make a simple integer ratio.
Lissajous figures are graphs of complex harmonic motion between parametric equations. To show how such a figure can be created, consider the. In order to accurately measure the central angles of lissajous figures, a standard and transparent circle, which is divided 72 equal circular arcs and is concentric with the lissajous figures, is pasted on the oscilloscopes display. Lissajous figures james emery 42008 contents 1curves 1 2 program 4 1curves let xta1 sin. This is an article about lissajous curves lissajous curves sometimes also known as lissajous figures or bowditch curves, are pretty shapes first investigated by nathaniel bowditch in 1815, and later and in much more detail by jules antoine lissajou in 1857. Liquid rope lissajous patterns annemarie aarts, vivi andasari, and stef van eijndhoven annemarie aarts is assistant professor of industrial mathematics at the technische universiteit eindhoven, the netherlands. Lissajous figure definition of lissajous figure by. The figures, sometimes called bowditch curves, were first described in the early 1800s by american mathematician nathaniel bowditch, who experimented with a pendulum undulating around perpendicular axes at the same time.
The resulting pattern was a function of theratio of the two frequencies. Named after jules antoine lissajous, a lissajous curve. A and b represent amplitudes in the x and y directions, a and b are constants, and. In mathematics, a lissajous curve lissajous figure or bowditch curve is the graph of a system of parametric equations. It can only run when the computer contains bios, and when the computer is booted.
If the ratios of their frequencies are rational, the curve will always eventually close. Lissajous figures where a 1, b n n is a natural number and. We can obtain very interesting graphs when each of the xand ycoordinates are given as functions of t. Lissajous figures a first course in electrical and. To use this catalogue, adjust the oscilloscope so that the x and y. To use lissajous figures to take frequency measurements. With a graphical user interface hand coded you can enter the parameters to generate a figure. The latex source files for this collection were created using an optical character recognition technology, and because of this process there may. This is a support page to the multimedia chapter interference and consonance in the volume waves and sound. Pdf in this research the researchers wanted to illustrate the physical materials about the lissajous curve which is often taught by teachers in.
899 114 526 114 352 1264 137 938 1119 141 1551 804 1429 391 18 182 1424 957 729 690 917 710 1083 841 38 700 1442 275 47 667 963 959 1256 1568 512 425 284 976 696 29 642 1182 1430 1443 540