SECOND-ORDER DIFFERENTIAL EQUATIONS IN THE PHASE PLANE

Abstract

The Second-Order Differential Equations in the Phase Plane was dealt by different scholars having various parameters. Second order differential equations occur while modeling the practical problems and determining the solution is not an easy task. The qualitative study of differential equations is concerned with how to deduce important characteristics of the solutions of differential equations without actually solving them. Many nonlinear effects in control systems, such as saturation, friction are best approximated by linear segmented characteristics rather than continuous mathematical functions. In this project the phase plane, simple pendulum, Autonomous equations in the phase plane, Energy transformation, energy conversion, damped oscillator which is used extensively for obtaining directly from the differential equation such properties as equilibrium, periodicity, stability, and so on. It has the advantage that it results in a phase plane divided up into different regions but with a linear differential equation describing the motion in each region.