On Mathematical Methods of Classical Mechanics

• Main Authors: Yi-Hsuan Cheng, 鄭亦玄
• Other Authors: Chen-Yun Lin
• Format: Others
• Language: en_US
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/77744319615061775155

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.