Date of Award
2024
Document Type
Thesis
Degree Name
Bachelors
Department
Natural Sciences
First Advisor
Kottke, Christopher
Second Advisor
Yildirim, Necmettin
Area of Concentration
Mathematics
Abstract
Despite its deterministic nature, chaos arises in many systems, including double pendulums. In this paper, we will provide the background information on differential equations along with foundational tools needed to detect chaos, such as the local stability analysis of steady states, time series, phase planes, and Lyapunov exponents. Armed with these tools, we will run numerical simulations, exploring the angular displacements for both single and double pendulums, and show why single pendulums are not considered chaotic. For double pendulums, we will estimate Lyapunov exponents for a given energy level to determine when chaos occurs.
Recommended Citation
Sivadanam, Sujit, "Chaotic Dynamics in Double Pendulums" (2024). Theses & ETDs. 6598.
https://digitalcommons.ncf.edu/theses_etds/6598