the superposition principle is used in model predictive control. The superposition principle can be applied when small deviations from a known solution to a nonlinear system are analyzed by linearization. In music, theorist Joseph Schillinger used a form of the superposition principle as one basis of his Theory of Rhythm in his Schillinger System of Musical Composition. In computing, superposition of multiple code paths, code and data, or multiple data structures is sometimes seen in shared memory, fat binaries, as well as overlapping instructions in highly optimized self-modifying code and executable text. History According to Léon Brillouin, the principle of superposition was first stated by Daniel Bernoulli in 1753: "The general motion of a vibrating system is given by a superposition of its proper vibrations." The principle was rejected by Leonhard Euler and then by Joseph Lagrange. Bernoulli argued that any sonorous body could vibrate in a series of simple modes with a well-defined frequency of oscillation. As he had earlier indicated, these modes could be superposed to produce more complex vibrations. In his reaction to Bernoulli’s memoirs, Euler praised his colleague for having best developed the physical part of the problem of vibrating strings, but denied the generality and superiority of the multi-modes solution. Later it became accepted, largely through the work of Joseph Fourier. See also Additive state decomposition Beat (acoustics) Coherence (physics) Convolution Green's function Impulse response Interference Quantum superposition References Further reading Superposition of sound waves External links Mathematical physics Waves Systems theory