lmat1261  2019-2020  Louvain-la-Neuve

Note from June 29, 2020
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
5 credits
22.5 h + 30.0 h
Q1
Teacher(s)
Language
French
Prerequisites

The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.
Main themes
Content
This course is a follow-up of LMAT1161 "Notions de physique mathématique". Its aim is to present an overview of the concepts of analytical mechanics.
The course's topics play an important role in other disciplines of the bachelors in physics and mathematics. Their presentation is adapted to the students of both these bachelors.
The course treats the following topics:
  1. Lagrangian mechanics
    • constrained systems, generalised coordinates;
    • d’Alembert principle, the Euler-Lagrange equations;
    • Hamilton's principle, elements of the calculus of variations;
    • symmetries and conservation laws.
       
  2. Hamiltonian mechanics
    • the Legendre transformation;
    • canonical equations of motion;
    • Poisson brackets;
    • canonical transformations.
       
  3. Hamilton-Jacobi theory
    • the Hamilton-Jacobi equation;
    • separation of variables;
    • action-angle variables;
    • towards quantum mechanics.
Evaluation methods
  • The student is evaluated through a written exam.
  • Through the active participation during the exercise sessions, any student may obtain a bonus of at most two points. These points are added to his exam's grade. 
Online resources
The course's Moodle website provides lecture notes, exercise sheets, a detailed syllabus and an ample bibliography.
Bibliography
  • Arnold, Mathematical methods of classical mechanics. Springer 1997

    Ouvrage à recommander aux étudiants avec une préférence pour la rigueur mathématique. Il est très détaillé et dépasse largement le cadre du cours.
     
  • Fomin, Calculus of variations. Dover Publications 2000.

    Ouvrage classique sur le calcul variationnel et ses applications à la mécanique classique, contient de nombreux exemples et exercices.
     
  • Landau, Lifshits, Cours de physique théorique. Tome 1 : Mécanique. Edition Mir 1994.

    Ceci est une référence standard pour physiciens. Il couvre tous les sujets des cours LMAT1161 et LMAT1261 (et bien plus), contient des exercices et leurs solutions.
     
  • Morin, Introduction to Classical Mechanics: With Problems and Solutions. Cambridge University Press 2008.

    Ouvrage récent très pédagogique, contient beaucoup d'exercices et leurs solutions.
     
  • Nolting, Theoretical Physics 2: Analytical mechanics.Springer-Verlag 2016.

    Ouvrage très pédagogique, contient beaucoup d'exercices et leurs solutions.
     
  • Goldstein, Classical mechanics. Addison-Wesley 2007.

    Référence classique pour physiciens avec de nombreux exemples, applications et exercices (sans solutions).
Teaching materials
  • matériel sur moodle
Faculty or entity


Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Aims
Bachelor in Mathematics

Bachelor in Physics

Additionnal module in Mathematics

Minor in Mathematics