Lissajous curves

In Fig. 3a,b are shown respectively the modulus of the measured magnetic induction and the computed one. In Fig. 3c,d we compare the modulus and the Lissajous curves on a line j/ = 0. The results show a good agreement between simulated data and experimental data for the modulus. We can see a difference between the two curves in Fig. 3d this one can issue from the Born approximation. These results would be improved if we take into account the angle of inclination of the sensor. This work, which is one of our future developpements, makes necessary to calculate the radial component of the magnetic field due to the presence of flaw. This implies the calculation of a new Green s function. 

Recording the applied av potential and the resulting ac current on a twin-beam oscilloscope produces Lissajous curves (in this case an ellipse), which may be used to the determine the impedances. Because of its frequency limitations and sensitivity to noise, this technique is not currently used in electrochemical measurements. 

Fig. 3.2 Lissajous curves for various phase differences the values of cp in degrees are shown in the legend...

Fig. 8 Dotted lines are the shear stress in the time domain measured at an excitation frequency of 1 Hz for different strain amplitudes ranging from 0.03 to 1. The temperature was set to T = 15.1 °Cto measure a glassy system. With increasing strain amplitude an increasing dissipative energy is measured, associated with an increasing area of the closed Lissajous curves. After exceeding the yield stress oy, that is indicated by the grey lines, the shear stress shows a distorted shape, which reflects the onset of nonlinearity. The MCT based predictions are depicted with full lines and show an overall good agreement with the experimental data, reprinted from Brader et al. [3], copyright 2010, American Physical Society...

A three-dimensional representation of an ion trajectory, shown in Figure 8, has the general appearance of a Lissajous curve composed of two fundamental frequency components, rUf O and >z,o of the secular motion. Higher-order (n) frequencies exist and the family of frequencies is described by given by... 

A process is forced by sinusoidal input m,). The output is a sine wave If these two signals arc connected to an x — y recorder, we get a Lissajous plot. Time is the parameter along the curve, which repeats itself with each cycle. The shape of the curve will change if the frequency is changed and will be different for different kinds of processes. 

Plotting Lissajous figures) Using a computer, plot the curve whose parametric equations are x(t) = sinr, y t) =sin(yf, for the following rational and irrational values of the parameter cu ... 

The resulting curves are called Lissajous figures. In the old days they were displayed on oscilloscopes by using two ac signals of different frequencies as inputs. 

Fig. 6.—Curve representing the motion of a system with two degrees of freedom, in which the two frequencies I l and I a are incommensurable (Lissajous figure).

More precisely the two energy surfaces A and B will intersect each other along a curve. The chance of predissociation for a vibration-rotation level of B will be great—apart from the fulfilment of selection rules perhaps introduced by the symmetry properties of the molecule—if its energy is about the same as that of a point on the intersection curve. For then the vibratory motion of the molecule represented by a sort of Lissajous figure on the surface V pa) come somewhere near the line of intersection with the surface V (p, pa) of A, making it easy for the molecule to jump from the former to the latter surface. 

Lissajous figures A curve in one plane traced by a point moving under the influence of two independent harmonic motions. In the common case the harmonic motions are simple, perpendicular to each other, and have a simple frequency ratio. They can be displayed by applying sinusoidal alternating potentials to the X- and Y-inputs of a cathode-ray oscilloscope. They are named after Jules Lissajous (1822-80). 

Another topic to establish a good TMDSC practice deals with Lissajous figures (or Bowditch curves), plots of the time-dependent heat-flow rate HF(t) or AT(t) versus... 

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