Date of Award

1-2019

Document Type

Thesis

Degree Name

Master of Science (MS)

College/School

College of Science and Mathematics

Department/Program

Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

Ashwin Vaidya

Committee Member

Eric Forgoston

Committee Member

Arup Mukherjee

Subject(s)

Least action, Pendulum

Abstract

The principle of least action is a variational principle that states an object will always take the path of least action as compared to any other conceivable path. This principle can be used to derive the equations of motion of many systems, and therefore provides a unifying equation that has been applied in many fields of physics and mathematics. Hamilton’s formulation of the principle of least action typically only accounts for conservative forces, but can be reformulated to include non-conservative forces such as friction. However, it can be shown that with large values of damping, the object will no longer take the path of least action. Through numerical simulation, this is shown to be true for two simple systems, an object in free fall and a harmonic pendulum, both linearly and cubically damped.

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