A lissajous curve, named after jules antoine lissajous is a. When the periods of motion in the two directions make a simple ratio, then a. Jules antoine lissajous 18221880 was a french physicist who was interested in waves, and around 1855. As part of the excel lissajous curve explorer i have included a gallery that you can scroll through to see a couple hundred of the best variations in my opinion that ive discovered thus far. Pdf discrete lissajous figures and applications researchgate. We will create a program that calculates the values of the x and y for. In this post i will show you how to calculate and plot the lissajous curves using c and gnuplot. Finite dehn surgery along acampos divide knots yamada, yuichi, 2006. 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. In example 1, we saw that the curve was an ellipse. In mathematics, a lissajous curve lissajous figure or bowditch curve is the graph of the system of parametric equations. Lissajous curves can also be generated using an oscilloscope. Through simulation of lissajous wave patterns using spreadsheets on microsoft excel can make it easier for students and teachers to understand the lissajous curve on the oscilloscope screen. Geometrical and graphical representations analysis of lissajous.
Lissajous and fourier knots marc soret and marina ville abstract we prove that any knot of r3 is isotopic to a fourier knot of type 1. Lissajouslike figures with triangular and square waves scielo. Mar 29, 2010 now we can plot an infinite number of lissajous curves using essentially no worksheet cells whatsoever. A labview based simulation of lissajous pattern using daq card.
Determining the signal frequency by lissajous curves and beats. 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. A labview based simulation of lissajous pattern using daq. A quick sketch that generates a lissajous curve using two randomly selected numbers from 010. 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. First studied by the american mathematician nathaniel bowditch in 1815, the curves were investigated independently by the french mathematician julesantoine lissajous in 185758. When the input to an lti system is sinusoidal, the output is. Lissajous is a complex audiovideo signal generator built in maxmsp and inspired by the work of jules antoine lissajous.
In mathematics, a lissajous curve lissajous figure or bowditch curve is the graph of a system of. How to draw 2d oscillations and lissajous curves using 3d projection. Lissajous figures or lissajous curves 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. In this particular example, because the output is 90 degrees out of phase from the input, the lissajous curve is a circle, and is rotating counterclockwise. If the periods are equal, the curve is always an ellipse. Lissajous curve generator version 2 openprocessing.
The added phase angle makes the curve run in a 90 degree angle a 270 degree angle will produce the same curve. 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. Trigonometryfor enthusiastslissajous figures wikibooks. Multivariate polynomial interpolation on lissajous. In mathematics, a lissajous curve lissajous figure or bowditch curve is the graph of a system of parametric equations. The larger of the numbers in the ratio now tells you the number of extrema to expect in the lissajous curve, when 1 is subtracted from it. A single point on each the lissajous figure and a second point. This displays a lissajous figure with a frequency ratio of 2. Another name that i found is the play curve of alice 1. In mathematical 29 terminology, a lissajous curve is a simple system of two 35 curve is highly dependent on the ratio ba, and. Now we can plot an infinite number of lissajous curves using essentially no worksheet cells whatsoever. When two pendulums that swing in perpendicular planes are used, the curve created will be a damped lissajous curve.
I have read somewhere that it is the least common multiple lcm of v and w but i. But it is said that the american nathaniel bowditch 17731838 found the curves already. By selecting a check box you may turn on a feature that also plots the derivative of the parametric curve. Lissajous a simple example of 2d line plot in matlab, and creating a gui without guide. In this particular example, because the output is 90 degrees out of phase from the input, the lissajous curve is a circle. This file contains additional information such as exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. Resulting lissajous curve when output is plotted as a function of the input. Nov 01, 2015 in the previous post, i considered the motion of a simple harmonic oscillator. This video explains how to determine possible parametric equations for a lissajous figure. We will create a program that calculates the values of the x and y for various values and for different n and store these values in a txt file.
The equations that describe these curves are the following. The figures form closed curves when the wavenumbers and are commensurable, i. But it is said that the american nathaniel bowditch 17731838 found the curves already in 1815. The relation of some lissajous curves to chebyshev polynomials is clearer to understand if the lissajous curve which generates each of them is. Its simple enough, but its hardly interesting once you look at it all of its observables displacement, velocity, acceleration and energy values are sinusoidal functions of time, and a rudimentary knowledge of trigonometric functions is more than sufficient to analyse its. If the ratio of their frequencies is a rational number 1. Note that there are two vcc and gnd pins on each module so youll end up running four wires from both the arduinos 5v output and its gnd pin finally, connect an oscilloscope to the zout2 outputs of the. Find the parametric equations for a lissajous curve.
Lissajous figures were first mentioned by nathaniel bowditch in 1815, and rediscovered by jules antoine lissajous in 1857. Named after jules antoine lissajous, a lissajous curve. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. Julesantoine lissajous 18221880 discovered these elegant curves in 1857 while doing his sound experiments.
A single point on each the lissajous figure and a second point on its derivative curve are highlighted based upon the value of the curve parameter allowing for correlation of the two curves. When the periods of motion in the two directions make a simple ratio, then a closed curve results. This ensures that the scaling is the same for the x and y axes. Let us compute the period of this curve, assuming that. Lissajous figures also called bowditch curve, pattern produced by the intersection of two sinusoidal curves the axes of which are at right angles to each other 1.
A harmonograph is a mechanical device that uses pendulums to control the movement of a pen andor to control the. In the example in curvilinear motion, the lissajous figure. Introduction to lissajous figures caroline teti, 2008 lissajous figures are patterns. As the fine wikipedia article 1 explains a lissajous curve is a parametric plot of sinusoids. Lissajous figure definition of lissajous figure by merriam. When the input to an lti system is sinusoidal, the output is sinusoidal with the same frequency, but it may have a different amplitude and some phase shift. Prior to modern electronic equipment, lissajous curves could be generated mechanically by means of a harmonograph. A lissajous curve, named after jules antoine lissajous is a graph of the following two. How to draw 2d oscillations and lissajous curves using 3d projection jan valek, petr sladek faculty of education, masaryk university, brno abstract this contribution presents possibilities of dynamic modelling that was developed using php for composition of perpendicular commensurable oscillations in plane. Esteve terradas 5, c3d007, 08860 castelldefels, spain.
Geometrical and graphical representations analysis of. 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. 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. Sinusoidal voltages are applied to the horizontal and vertical deflection plates, they have the form v a sin. Pdf drive investigated dozens of problems and listed the biggest global issues facing the world today. Geometrical and graphical representations analysis of lissajous figures in rotor dynamic system hisham a. Multivariate polynomial interpolation on lissajouschebyshev. Abstractour present work focuses on the beautiful but simple technique for determination of the speed of sound using analysis of the lissajous patterns.
Pdf in this paper, an innovative method based on an algorithm utilizing discrete convolutions of discretetime functions is developed to obtain. Lissajous figures, triangular and square waves, fourier analysis. Lissajous curves take certain common shapes depending on the values of the variables in the expressions. How to draw 2d oscillations and lissajous curves using 3d. Press any key to stop the generation and save the curve as an image in your sketch folder. Parametric plots use a parameter say t to calculate the the x and y coordinates xt, yt. Lissajous figures also called bowditch curve, pattern produced by the intersection of two sinusoidal curves the axes of which are at right angles to each other.
A lissajous curve is formed when two sine waves plotted on their respective x and y axes. After him the curve bears the name of bowditch curve. This lissajous curve is illustrated using a spreadsheet program on a computer or laptop. 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. Lissajous figure definition of lissajous figure by. Askari2 1 faculty of science, engineering and computing. As part of the excel lissajous curve explorer i have included a gallery that you can. Permission is granted to copy, distribute andor modify this document under the terms of the gnu free documentation license, version 1.
The process of manual calculation of the above mentioned equations would be very lengthy. I have read somewhere that it is the least common multiple lcm of v and w but i do not understand what this means. Changes for this version include the line gradually changing colors, centering the curve around the mouse position, and clearing the screen when the mouse button is clicked. This is produced by hitting an upright tuning fork with a frequency of 256 hz, and then hitting a tuning fork that is laid on its.
Lissajous curves and after the epitrochoids, were going to see another family of wonderful figures. Lissajous used a narrow stream of sand pouring from the base of a compound pendulum to produce the curves ratio of the two frequenc1, 2. A lissajous curve is used in experimental tests to determine if a device may be properly categorized as a memristor. You can see one using an oscilloscope and a couple of signal generators, if you play with one of those. This is a support page to the multimedia chapter interference and consonance in the volume waves and sound. Measurement of the speed of sound in air medium using. Exploring variable effects in a system of parametric equations. Lissajous curves can also be generated using an oscilloscope as illustrated. Lissajous figures james emery 42008 contents 1curves 1 2 program 4 1curves let xta1 sin. The media project is born with the purpose of investigating the relationship.
Lissajous figures are created by combining a periodic motion in one direction with a periodic motion in a perpendicular direction. At each instant, the scope plots a dot with the input x sample as the horizontal coordinate and the output. The maximum period of a lissajous curve is 2 pi, and i do not understand how lcmv,w would yield a value less than 2 pi. Lissajous figures are easily written in parametric form as. We show a generalization of the wellknown lissajous figures, changing the two orthogonal. An octopus circuit can be used to demonstrate the waveform images on an oscilloscope. Generating lissajous curves it is a truth universally acknowledged, that a person in possession of an oscilloscope must draw lissajous curves. A lissajous curve, named after jules antoine lissajous is a graph of the following two parametric equations load more similar pdf files. If one period is twice the other, we get a quartic curve. A harmonograph is a mechanical device that uses pendulums to control the movement of a pen andor to control the movement of the drawing paper. Two phaseshifted sinusoid inputs are applied to the oscilloscope in xy mode and the phase relationship between the signals is presented as a lissajous figure.