الملخص

This paper devoted to study the stability of periodic motion for physical application which is leads to differential equations of second order )Double and Spherical Pendulum( respectively by using the stability of equilibrium position given by Laypunov and Ghetagev's methods which depends on principle of energy conservation, also we will describe periodic motion and explain the phase plane )The trajectory of solutions( and state of the stability for double and spherical pendulum by using )Maple(.