Newton's seventeenth century laws of motion. For two hundred years interest in vibration was limited to the period of the pendulum and the movements of the planets and the tides; but by the end of the nineteenth century machinery had been invented that really vibrated, as a result of high speed mechanisms, shaking and rattling to the point of destroying themselves and requiring from theoreticians and experimentalists some serious attention. John William Strutt, known more familiarly in science as Lord Rayleigh (1842-1919) developed and organized the beginnings of modern mechanical vibration theory, and his work was followed by the contributions of Timoshenko and others in the mid-20th century.
Any contrivance of physical components, such as a simple pendulum or a complex machine, subject to vibration can be described by six coordinates, three to describe its x, y, and z linear positions, and three more to describe its angles of displacement from the x, y, and z axes. The
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