Date of Award

5-2026

Document Type

Thesis

Degree Name

Master of Science (MS)

College/School

College of Science and Mathematics

Department/Program

Mathematics

Thesis Sponsor/Dissertation Chair/Project Chair

Ashwin Vaidya

Committee Member

Jonathan Cutler

Committee Member

Arup Mukherjee

Abstract

Autorotation is the spontaneous rotation of an object, usually caused by an external fluid flow. The study of autorotation has many physical applications, such as in the design of wind/water turbines. In this thesis, we explore a nonlinear pendulum ordinary differential equation (ODE) which is used to model rotating plates in a fluid and has the capacity to reveal autorotation. In the context of an ODE, autorotation emerges as a bifurcation past oscillations, when the initial velocity of the system crosses a particular threshold. In his classic study from 1983, Lugt [14] utilizes this equation to capture experimental autorotation. Copeland’s 1994 study [7] follows Lugt’s model, classifying the various motions of a pendulum subject to nonlinear autorotating forces. This thesis entails a deeper study following Lugt’s and Copeland’s analysis, involving: (a) comparisons to different rudimentary and sophisticated pendulum models; (b) a phase-space analysis of the behavior-defining limit cycles that describes two regions previously not identified in the literature, and (c) a study of the instantaneous period and envelopes of select solutions to the model.

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