Renormalizing the Simple Pendulum
Copyright policy )Renormalizing the Simple Pendulum
Summary: The authors present an elementary scheme for calculating the period of oscillation or rotation of a simple pendulum. It is based on the invariance of the complete elliptic integral of the first kind under the arithmetic-geometric mean iteration. They explain how this scheme can be interpreted as an example of renormalization, a technique with many recent applications in both physics and applied mathematics.
Free motion of a rigid body, Phase plane analysis, limit cycles for nonlinear problems in mechanics, Elliptic functions and integrals, Local and nonlocal bifurcation theory for dynamical systems, complete elliptic integral of the first kind, arithmetic-geometric mean iteration, period of oscillation, renormalization
Free motion of a rigid body, Phase plane analysis, limit cycles for nonlinear problems in mechanics, Elliptic functions and integrals, Local and nonlocal bifurcation theory for dynamical systems, complete elliptic integral of the first kind, arithmetic-geometric mean iteration, period of oscillation, renormalization
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