Course Information

Course Information

In this web page we provide the syllabus of the course Classical Mechanics II, offered by the Department of Physics.

The list of the courses offered during the current accademic year is available here. 

The list of all courses offered by the Department of Physics is available here.

Code Φ-501
Title Classical Mechanics II
Category B
ECTS 6
Hours 6
Level Graduate
Semester Spring
Teacher G. Pavlou
Program
Course Webpage https://eclass.physics.uoc.gr/courses/PH501/
Goal of the Course

The course is intended for graduate and advanced undergraduate students and serves as an extension of an introductory Newtonian classical mechanics course. It covers topics that constitute the core of mechanics, such as Lagrange equations, Lagrange multipliers, Hamilton's principle, Hamilton equations, canonical transformations, and Hamilton-Jacobi theory. Emphasis is placed on analytical techniques as well as practical applications. 
 
Syllabus

Principle of Least Action, Calculus of Variations, Introduction to the Lagrangian Function, Euler-Lagrange Equations. 
Applications: Light propagation in a medium, the brachistochrone problem. 
Construction of the Lagrangian from Symmetries, Generalized Coordinates, Constrained Motion, Lagrange Multipliers. 
Applications: Harmonic Oscillator and the motion of a charged particle in an electromagnetic field. 
The Concept of Symmetry, Noether’s Theorem, Conservation of Momentum and Angular Momentum. 
Small Oscillations, Normal Frequencies, Normal Modes of Oscillation. 
Hamiltonian Formalism, Legendre Transformation, Hamilton’s Equations. 
Liouville’s Theorem, Applications in Statistical Mechanics. 
Canonical Transformations, Poisson Brackets. 
Hamilton-Jacobi Theory, Adiabatic Invariants, Action-Angle Variables. 
Advanced Topics: Classical Field Theory, Quantum Mechanics, and Path Integrals.
Bibliography

1.Theoretical Mechanics – 2nd Edition, Theoharis Apostolatos & Petros Ioannou, National and Kapodistrian University of Athens (EKPA). 
Classical Mechanics, Goldstein, Poole & Safko, Addison-Wesley. 
2.Emmy Noether’s Wonderful Theorem, D. E. Neuenschwander, Johns Hopkins University Press, 2011. 
3.Lecture Notes on Classical Dynamics, David Tong, University of Cambridge. 
The Classical Theory of Fields: Volume 2, 4th Edition, L.D. Landau, E.M. Lifshitz