Modeling Automata with Classical Mechanics


A model of a moving mechanical device known as automata is carried out with an analytically solved system of differential equations. The system of equations used is that of two masses coupled through a spring. The system is solved by considering a center of mass - relative coordinate approach. Once a solution of the relative coordinate is effected, each mass's coordinate is obtained as a function of time. To model the automata one has to keep in mind that the spring must have an equilibrium length so as to mimic movement and to prevent the masses from overlapping. The masses in this model take the place of the automata's head and tail, respectively. Once initial conditions are provided, the masses' positions versus time are animated so as to simulate the automata's motion.

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