2013
DOI: 10.1590/s1806-11172013000300031
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Lissajous-like figures with triangular and square waves

Abstract: We show a generalization of the well-known Lissajous figures, changing the two orthogonal simple harmonic oscillations to triangular and square-wave-type oscillations. All figures cross the origin of axes when there is no phase difference between the oscillations. Aside from this common feature, square-wave-type figures show a very different behavior, with discontinuous phase changes and impossibility of using a simple formula to get the frequency ratio between the two component oscillations.

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Cited by 6 publications
(7 citation statements)
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“…When the waves are at a phase angle of exactly π /2, the output shape is a distorted ellipse. Various distorted ellipses can be observed between these two extremes [ 15 ].…”
Section: Sample Preparation and Experimental Setupmentioning
confidence: 99%
“…When the waves are at a phase angle of exactly π /2, the output shape is a distorted ellipse. Various distorted ellipses can be observed between these two extremes [ 15 ].…”
Section: Sample Preparation and Experimental Setupmentioning
confidence: 99%
“…An important issue is the development of tools, machine tools, and honing methods which, for example, would allow the creation of oil paths in the shape of curves of various kinds [156][157][158]. It is also very important to control the value of temperature created in final step of the honing process.…”
Section: Effect Of Honing Parameters On Shape Deviations In the Honed...mentioning
confidence: 99%
“…Os primeiros estudos destas curvas foram desenvolvidos por Bowditch e Lissajous durante o Século XIX [7]. Atualmente elas são utilizadas em diversas aplicações, tanto de cunho didático quanto tecnológico, como por exemplo para obter a frequência de um sinal desconhecido, ou determinar a diferença de fase entre dois sinais [8].…”
Section: Figuras De Lissajousunclassified