Studi Kualitatif Persamaan Rayleigh

Abstract

Rayleigh's equations have many applications in physics and electromechanics. In the field of physics can be seen such as optics, vibration systems, sound, wave theory, color vision, electrodynamics, electromagnetism, light scattering, fluid flow, hydrodynamics, photography, as well as waves and frequencies, also applied in the fields of health, agriculture, biology, astronomy. This study aims to determine the fixed point and prove the existence of a periodic solution and analyze the condition of the Rayleigh equation system around the fixed point. The Rayleigh equation is transformed into a first-order differential equation to obtain a fixed point, and using an approximation to the Van Der Pool equation it is proved that the Rayleigh equation has a single periodic solution. The Rayleigh equation has one periodic solution and has one fixed point, the origin. The condition of the system around a fixed point is said to be unstable which is shown analytically by changing the value of the parameter to the eigenvalues. Geometrically it is shown that the phase portrait moves away from a fixed point and exits towards the periodic solution where the periodic solution is said to be stable.