page_title: Christiaan Huygens
section_title: Pendulums
hierarchical_section_title: Christiaan Huygens / Work in natural philosophy / Horology / Pendulums
caption_attribution_description: Nederlands: Klok ontworpen door Christiaan Huygens (1629 - 1695). English: Clock designed by Christiaan Huygens (1629 - 1695) signed by Salomon Coster (16?? - 1659).
context_page_description: Christiaan Huygens FRS, also spelled Huyghens, was a Dutch physicist, mathematician, astronomer and inventor, who is widely regarded as one of the greatest scientists of all time and a major figure in the scientific revolution. In physics, Huygens made groundbreaking contributions in optics and mechanics, while as an astronomer he is chiefly known for his studies of the rings of Saturn and the discovery of its moon Titan. As an inventor, he improved the design of the telescope with the invention of the Huygenian eyepiece. His most famous invention, however, was the pendulum clock in 1656, which was a breakthrough in timekeeping and became the most accurate timekeeper for almost 300 years. Huygens was an outstanding mathematician and, because he was the first to transfer mathematical inquiry to describe unobservable physical phenomena, he has been called the first theoretical physicist and the founder of modern mathematical physics.
  In 1659, Huygens was the first to derive geometrically the now standard formulae for the centripetal force and centrifugal force in his work De vi centrifuga. The formulae played a central role in classical mechanics.
context_section_description: In 1673 Huygens published Horologium Oscillatorium sive de motu pendulorum, his major work on pendulums and horology. It had been observed by Mersenne and others that pendulums are not quite isochronous: their period depends on their width of swing, with wide swings taking slightly longer than narrow swings.
  Huygens analyzed this problem by finding the curve down which a mass will slide under the influence of gravity in the same amount of time, regardless of its starting point; the so-called tautochrone problem. By geometrical methods which were an early use of calculus, he showed it to be a cycloid, rather than the circular arc of a pendulum's bob, and therefore that pendulums are not isochronous. He also solved a problem posed by Mersenne: how to calculate the period of a pendulum made of an arbitrarily-shaped swinging rigid body. This involved discovering the centre of oscillation and its reciprocal relationship with the pivot point. In the same work, he analysed the conical pendulum, consisting of a weight on a cord moving in a circle, using the concept of centrifugal force.
  Huygens was the first to derive the formula for the period of an ideal mathematical pendulum (with massless rod or cord and length much longer than its swing), in modern notation:
  with T the period, l the length of the pendulum and g the gravitational acceleration. By his study of the oscillation period of compound pendulums Huygens made pivotal contributions to the development of the concept of moment of inertia.
  Huygens also observed coupled oscillations: two of his pendulum clocks mounted next to each other on the same support often became synchronized, swinging in opposite directions. He reported the results by letter to the Royal Society, and it is referred to as "an odd kind of sympathy" in the Society's minutes. This concept is now known as entrainment.
caption: Huygens' clock, Rijksmuseum, Amsterdam
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