A survey to Analytical Mechanics

Abstract

The scope and Aim of Mechanics is the science of motion. It has a twofold object: First, to describe the motions of bodies an interpret, them by means of a few laws and principles, which are generalizations derived from observation and experience. Second ,to predict the motion of bodies for all times when the circumstances of the motion for any one instant are given ,in addition to the special laws which govern the motion . This research aims to cover some of these concepts, and it is organized and divided in two chapters:- In chapter one, we discuss the Newton Mechanic’s, and the equations of motion according to Newton laws of motion and their solution. Also we study the Lagrangian mechanics and law, and we explain the concepts’ of the action and symmetries with some applications and examples. In the last chapter, we illustrate the concept of the conic section; also we study the central force two body problems with some applications and examples.