2024/03/05 by Javier Jiménez López, López, Javier Jiménez, Víctor J. García‐Garrido +1 · 4 citations
Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2403.07000
openalex publication_date 2024/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we apply the method of Lagrangian descriptors as an indicator to study the chaotic and regular behavior of trajectories in the phase space of the classical double pendulum system. In order to successfully quantify the degree of chaos with this tool, we first derive Hamilton's equations of motion for the problem in non-dimensional form, showing that they can be written compactly using matrix algebra. Once the dynamical equations are obtained, we carry out a parametric study in terms of the system's total energy and the other model parameters (lengths and masses of the pendulums, and gravity), to determine the extent of the chaotic and regular regions in the phase space. Our numerical results show that for a given mass ratio, the maximum chaotic fraction of phase space trajectories is attained when the pendulums have equal lengths. Moreover, we give a characterization of the growth and decay of chaos in the system in terms of the model parameters, and explore the hypothesis that the chaotic fraction follows an exponential law over different energy regimes.