The Principle of Variational Method and The Use of Variational Method to Solve Practical Problems

This article tries to obtain and use the fundamental principle of analytical mechanics—variational method, which is practical application of calculus. With the development of mathematic and physics, more people want to use advanced mathematics to solve practical problems. Hence, variational method has been developed. The article analyzed two circumstance after obtaining the Euler—Lagrange equation and the first integral. Obtaining the most rapid descent line is also an application of mathematical modeling, which is a classical application of mathematic. The article will focus on two classical circumstance, using the variable methods, and the basic logic of the methods.