FYS-4406 Analytical Mechanics, 5 cr


Suitable for postgraduate studies.


Jouko Nieminen


Toteutuskerta Periodi Vastuuhenkilö Suoritusvaatimukset
FYS-4406 2019-01 1 - 2 Joonas Keski-Rahkonen
Jouko Nieminen
The total mark is determined based on a final exam, practical work assignments, and the student's activity in exercise classes and group projects:

1) There will be only 9 double lectures. They are intended to give an introduction to the concepts and methods used in analytical mechanics. First period, Monday 10-12 at SJ212A. Final exam 40% of the points to determine the grade.

2) In addition, there are 13 assignment sessions, for practicing problem solving techniques, going through central examples of Lagrange and Hamilton mechanics, as well as nonlinear dynamics and chaos theory. In addition, there will be numerical assignments. Assignments 50%

3) As the assignments may be sometimes like small projects, the 13 weekly exercises are meant for shorter problems and applications of theory. Exercises 10%


After passing the course, the student is acquainted with advanced formulations and methods of classical mechanics and can construct problems of physics in the framework of variational calculus. In addition to analytic skills, the student has the basic skills in numerical simulation of classical mechanics systems. Furthermore, the student has introductory skills to analyzing and solving nonlinear problems in physics.


Sisältö Ydinsisältö Täydentävä tietämys Erityistietämys
1. Equations of motion and conservation laws. The two complementary approaches in mechanics: direct solution of time dependencies and first integrals from conserving quantities.      
2. Lagrangian and Hamiltonian methods in physics and variational approaches.   Formulation and solution of field equations using variational methods. Correspondencies between classical and quantum mechanics.   
3. Nonlinearity and chaos. Attractors, limit cycles, Hopf Bifurcations.      
4. Numerical solutions of equations of motion derived using Lagrangian and Hamiltonian methods. Molecular dynamics method.  Stability considerations. Numerical solution of chaotic systems and Poincare maps.   

Ohjeita opiskelijalle osaamisen tasojen saavuttamiseksi

The total mark is determined based on a final exam (40%), practical work assignments (50%), and the student's activity in exercise classes (10%).


Numerical evaluation scale (0-5)


Tyyppi Nimi Tekijä ISBN URL Lisätiedot Tenttimateriaali
Book   Classical Mechanics   T.W.B. Kibble and F.H. Berkshire         Yes   


Opintojakso ei vastaan mitään toista opintojaksoa

Päivittäjä: Kunnari Jaana, 05.03.2019