Pendulum Integration and Elliptic Functions
P.L. Garrido, G. Gallavotti
TL;DR
This paper revisits the classical pendulum's integration near its unstable equilibrium, constructing normal hyperbolic canonical coordinates to enhance understanding of its dynamics.
Contribution
It introduces a novel method for integrating the pendulum's equations using hyperbolic canonical coordinates, providing new insights into its behavior.
Findings
Successful construction of hyperbolic canonical coordinates
Enhanced understanding of pendulum dynamics near unstable equilibrium
Potential applications to nonlinear dynamical systems
Abstract
Revisiting canonical integration of the classical pendulum around its unstable equilibrium, normal hyperbolic canonical coordinates are constructed
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Quantum chaos and dynamical systems · Control and Stability of Dynamical Systems