CLASSICAL MECHANICS

This lesson on the subject of classical mechanics, it is aimed at students of Pure and Applied Sciences. The first three chapters and the fifth are related to the motion of the material point. Especially in the first chapter the motion of a particle in one and two dimensions is described, while the second is a qualitative study of one-dimensional motion with particular emphasis on linear oscillations of the material point. In the third chapter we discuss the central movements. Finally, at the fifth chapter the motion of a point relative to non-inertial reference system is considered and the conclusions are applied to the motion of a point in regard to the rotating Earth. The fourth chapter examines the movement system of particles, as well as the movement of bodies with variable mass, while at the sixth chapter the motion of a rigid body is studied. The last three chapters are introductory in Analytical Mechanics, that is, the study of the motion of bodies with the method of Lagrange. Especially in the seventh chapter the principle of virtual work and the principle of the D 'Alembert for a material point and for a system of particles are presented, while at the last two chapters Lagrange equations (normal equations) are also presented.

Objectives

At the end of this course the student should be able to 1. To be able to describe the motion of material point (particle). 2. To know the basic laws of Newtonian Mechanics. To apply them to physical problem as, oscillations, central force fields, etc. 3. To be able to describe the motion of a system of material points (particles). 4. To be able to describe the motion of a rigid body. 5. To be able to describe motions at non inertial coordinate systems. 6. To be able to describe physical systems with formalism of Analytical Mechanics. 7. To be able to define the physical problem, the mathematical problem and to select the suitable method for the solution, and after that to valuate and interpret the results. 8. To be able to apply the basic laws of Mechanics to Celestial Mechanics, Quantum Mechanics, etc.

Prerequisites

There are no prerequisite courses. It is however recommended that students should have at least a basic knowledge of Vector Analysis, Analytical Geometry, Ordinary Differential Equations and Partial Differential Equations.

Syllabus

1. Kinematics of material point (particle) 2. The laws of Newtonian Mechanics 3. One dimension motions - Oscillations 4. Central force field 5. Systems of material points (particles) 6. Non inertial coordinate systems 7. Constraints – Principle of virtual work – D’ Alembert’ principle 8. Lagrange’s equations 9. Hamilton theory. Poisson brackets. The principle of least action