In physics and mathematics, in the area of dynamical systems, a double pendulum is a pendulum with another pendulum attached to its end, and is a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions. The motion of a double pendulum is governed by a set of coupled ordinary differential equations. For certain energies its motion is chaotic.

Several variants of the double pendulum may be considered; the two limbs may be of equal or unequal lengths and masses, they may be simple pendulums or compound pendulums (also called complex pendulums) and the motion may be in three dimensions or restricted to the vertical plane. In the following analysis, the limbs are taken to be identical compound pendulums of length Failed to parse (Missing texvc executable; please see math/README to configure.): \ell

, and the motion is restricted to two dimensions.

In a compound pendulum, the mass is distributed along its length. If the mass is evenly distributed, then the centre of mass of each limb is at its midpoint, and the limb has a moment of inertia of Failed to parse (Missing texvc executable; please see math/README to configure.): \textstyle I=\frac{1}{12} m \ell^2

Steven Henry Strogatz /ˈstroʊɡæts/ (born August 13, 1959, Torrington, Connecticut) is an American mathematician and the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University. He is known for his contributions to the study of synchronization in dynamical systems, and for his work in a variety of areas of applied mathematics, including mathematical biology and complex network theory.

In particular, his 1998 Nature paper with Duncan Watts, entitled "Collective dynamics of small-world networks", is widely regarded as a seminal contribution to the interdisciplinary field of complex networks, whose applications reach from graph theory and statistical physics to sociology, business, epidemiology, and neuroscience. As one measure of its importance, it was the most highly cited article about networks between 1998 and 2008, and the sixth most highly cited paper in all of physics.

Strogatz's writing includes the 1994 textbook Nonlinear Dynamics and Chaos, two popular books, and frequent newspaper articles. His most recent book, published in 2009, was The Calculus of Friendship, called "a genuine tearjerker" and "part biography, part autobiography and part off-the-beaten-path guide to calculus". His trade book Sync was chosen as a Best Book of 2003 by Discover Magazine. Strogatz also filmed a series of lectures on chaos theory for the Teaching Company, released in 2008, and, in late January 2010, Strogatz began writing a weekly column on mathematics in The New York Times. These columns, along with many others penned by Strogatz, will appear in a book slated for release in 2012. The New York Times columns have been described as "must reads for entrepreneurs and executives who grasp that mathematics is now the lingua franca of serious business analysis."