Senior Project Advisor
Tilmann Glimm
Document Type
Project
Publication Date
Spring 2023
Keywords
Math, Lagrangian Mechanics, Rigid Body, Rigid Body Motion, Physics
Abstract
This paper begins by deriving the equations of motion for the Lagrangian formulation of mechanics. Lagrangian mechanics describes the same thing as the traditional Newtonian mechanics (which is what is taught in most undergrad physics classes), but rather than model the system through forces, it models the system through energy. Energy is conserved in a system, which allows the Lagrangian formulation to model certain types of systems in a more efficient way than the Newtonian formulation.
Next, the paper explores rigid body motion, specifically looking at the motion of the angular momentum. The goal of this part is to explain what causes an object to flip back and forth when it is rotating about one of its axes in zero gravity. To help demonstrate why this happens, there is a specific example of a t-handle exhibiting such motion. The t-handle in this paper is simply two cylinders, one resting horizontally atop the other, forming a sort of 'T' shape This example reveals that changing the dimensions of the t-handle will change how the body moves as it rotates about specific axes.
Department
Mathematics
Recommended Citation
Maurer, Eric, "Lagrangian Mechanics and the Motion of a T-Handle" (2023). WWU Honors College Senior Projects. 698.
https://cedar.wwu.edu/wwu_honors/698
Type
Text
Rights
Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.
Language
English
Format
application/pdf