Skip to content
Main menu hidden.

Analytical Mechanics

  • Number of credits 7.5 credits
  • Level Bachelor's level
  • Starting Spring Term 2025

About the course

The course deals with motion relative to an accelerated reference frame, variable mass systems, calculus of variations, Lagrange and Hamilton dynamics with an introduction to Poisson brackets, central motion, coupled oscillations, and rigid body dynamics in three dimensions including the inertia tensor, Euler angles and Euler's equations.
The emphasis is on the Lagrange formulation of classical mechanics.
Furthermore, canonical transformations and the Hamilton-Jacobi equation are discussed.

Expected study results
After completing the course, the student should be able to:  

  • account for central elements such as relative motion, Lagrange's and Hamilton's equations, central motion, coupled oscillations and rigid body dynamics,
  • derive important results in the above areas, such as Lagrange's equations, the equations of motion in small oscillations and the rigid body's equations of motion,
  • write down Lagrange's equations for different physical situations, and, in simpler cases, solve them,
  • write down the equations of motion for coupled systems, and solve them for small oscillations,
  • write down the equations of motion for a rigid body, and, in simpler cases, solve them
  • calculate a particle's movement in a rotating reference system,
  • write down and solve the equations of motion for central motion,
  • apply the Hamilton-Jacobi method to solve separable problems.

Form of instruction
The teaching is conducted in the form of lectures and problem solving sessions.

The examination of the course is in the form of an individual, written exam at the end of the course. The grading scale for the written exam is Fail (U), Pass (3), Pass with Merit (4), Pass with Distinction (5). The grade of the exam determines the grade of the course.
A student who have passed the examination is not allowed to take another examination in order to get a higher grade.

Classical dynamics of particles and systems
Thornton Stephen T., Marion Jerry B.
5. ed. : Belmont, Calif. : Brooks/Cole - Thomson learning : cop 2004 : xvi, 656 s. :
ISBN: 0-534-40896-6

Application and eligibility

Analytical Mechanics, 7.5 credits

Det finns inga tidigare terminer för kursen Spring Term 2025 Det finns inga senare terminer för kursen


15 April 2025


8 June 2025

Study location




Type of studies

Daytime, 67%

Required Knowledge

Mathematical Methods of Physics 15 credits (or Differential Equations 7,5 credits and Calculus in Several Variables 7,5 credits) and. Classical Mechanics 9 credits.

Entry requirements


Academic credits Applicants in some programs at Umeå University have guaranteed admission to this course. The number of places for a single course may therefore be limited.

Application code



The online application opens 16 September 2024 at 13:00 CET. Application deadline is 15 October 2024. How to apply

Application and tuition fees

As a citizen of a country outside the European Union (EU), the European Economic Area (EEA) or Switzerland, you are required to pay application and tuition fees for studies at Umeå University.

Application fee

SEK 900

Tuition fee, first instalment

SEK 17,850

Total fee

SEK 17,850

Contact us

Please be aware that the University is a public authority and that what you write here can be included in an official document. Therefore, be careful if you are writing about sensitive or personal matters in this contact form. If you have such an enquiry, please call us instead. All data will be treated in accordance with the General Data Protection Regulation.

Course is given by
The Department of Physics
Contactperson for the course is:
Michael Bradley