| Summary: | 碩士 === 國立臺灣大學 === 數學研究所 === 103 === 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.
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