Sentence examples for modulation equations that from inspiring English sources

By introducing an approximation based on Jacobian elliptic functions we derive an approximate set of two nonlinear integro-differential modulation equations that govern the time evolution of the amplitude and phase of the motion of the attachment.

The method of multiple scales is used to obtain four first order ordinary differential equations that describe the modulation of the amplitudes and phases of vibrations in the horizontal and vertical directions.

The method of multiple scales is used to derive two first-order ordinary differential equations that describe the modulation of the amplitude and the phase of the response with the non-linearity and both resonances.

Long-Thee histories, phase planes, Poincaré methodand spectra of the responses are presented.

It is found that the amplitude modulation equations are equal to normal forms equations available in the literature.

Amplitude and phase modulation equations are derived.

The effects of the position Amplitudetude of the mand, as well as effects of different end conditions on the vibrations, are determined.

The amplitude and phase modulation equations are presented.

The amplitude and phase modulation equations are derived.

The frequency-response equation is derived from the amplitude modulation equations.

The equilibrium solutions, the periodic solutions and chaotic solutions of the modulation equations are also investigated.