On Mathematical Methods of Classical Mechanics
Date Issued
2015
Date
2015
Author(s)
Cheng, Yi-Hsuan
Abstract
In this thesis, I give a survey of mathematical methods of classical mechanics. Classical mechanics consists of Newtonian, Lagrangian, and Hamiltonian mechanics. Newtonian mechanics is enlightened by Galileo’s principle of relativity, so I give mathematical construction of this principle in the beginning. By methods in Newtonian mechanics, I have shown that every three-dimensional motion in a central force field remains in some plane. By Lagrange’s equations in Lagrangian mechanics, I have solved the motion of two point masses with fixed distance. Through a variational principle, I have shown how a Lagrangian mechanical system generalizes a Newtonian potential mechanical system. Then by Legendre transformation, I have shown how a Lagrangian mechanical system is a particular Hamiltonian mechanical system.
Subjects
Lagrangian mechanics
Hamiltonian mechanics
central force field
Newtonian potential mechanical system
Legendre transformation
Type
thesis
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ntu-104-R00221023-1.pdf
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