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Εικόνα επιλογής

Κλασική Μηχανική II

(Φ-501) -  Γεώργιος Ε. Παύλου

Περιγραφή Μαθήματος

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.

ECTS Credits: 6

Class Hours for the Spring Semester (Spring Semester 2024-2025):

  • Monday, 15:00 - 17:00, Seminar Room, 2nd Floor, Physics Building
  • Thursday, 14:00 - 16:00, Seminar Room, 2nd Floor, Physics Building
  • Friday, 14:00 - 16:00, Seminar Room, 2nd Floor, Physics Building

First Meeting: Monday, 10/02/2025

Ημερομηνία δημιουργίας

Τρίτη 18 Ιανουαρίου 2022

Σελίδα μαθήματος
  • Περίγραμμα

    Information

    Instructor: Georgios E. Pavlou

    Office: Room 235, Physics Building

    Email: gepavlou@physics.uoc.gr

    Website: https://orcid.org/0000-0003-4478-935X

    Class Hours for the Spring Semester:

    • Monday, 15:00 - 17:00, Seminar Room, 2nd Floor, Physics Building
    • Thursday, 14:00 - 16:00, Seminar Room, 2nd Floor, Physics Building
    • Friday, 14:00 - 16:00, Seminar Room, 2nd Floor, Physics Building

    Course Topics:

    • 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.

    Recommended Textbooks:

    • Theoretical Mechanics – 2nd Edition, Theoharis Apostolatos & Petros Ioannou, National and Kapodistrian University of Athens (EKPA).
    • Classical Mechanics, Goldstein, Poole & Safko, Addison-Wesley.
    • Emmy Noether’s Wonderful Theorem, D. E. Neuenschwander, Johns Hopkins University Press, 2011.
    • Lecture Notes on Classical Dynamics, David Tong, University of Cambridge.
    • Classical Mechanics (5th Edition), Tom W B Kibble, Frank H Berkshire
    • The Classical Theory of Fields: Volume 2, 4th Edition, L.D. Landau, E.M. Lifshitz

    Student Assessment:

    • Written examination (70% of the final grade).
    • Mandatory assignment submissions (30% of the final grade).