A gyroscope is a device for measuring or maintaining orientation, based on the principles of conservation of angular momentum. The device is a spinning wheel or disk whose axle is free to take any orientation. This orientation changes much less in response to a given external torque than it would without the large angular momentum associated with the gyroscope's high rate of spin. Since external torque is minimized by mounting the device in gimbals, its orientation remains nearly fixed, regardless of any motion of the platform on which it is mounted. A new method of optimization, particle swarm optimization (PSO), is able to accomplish the same goal as GA optimization in a new and faster way. The purpose of this paper is to investigate the foundations and performance of the two algorithms when applied to  solve of gyroscope equation.