Analytical Mechanics 7.5 credits

About the course

Content 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.

Examination 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.

Literature 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

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Spring 2026
- Analytical Mechanics
  
  Second admissions round for EU/EEA citizens
  
  Spring 2026 / Umeå / English / On site
  
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  Starts
  10 April 2026
  
  Ends
  7 June 2026
  
  Number of credits
  7.5 credits
  
  Type of studies
  On site
  
  Study pace
  67%
  
  Teaching hours
  Daytime
  
  Study location
  Umeå
  
  Language
  English
  
  Application code
  UMU-53102
  
  Eligibility 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.
  
  Selection
  Academic credits
  
  Application
  Online applications are now open. Application deadline is 15 October 2025. Please note: This second application round is intended only for EU/EEA/Swiss citizens.
  
  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 19,038
  
  Total fee: SEK 19,038
  
  Details about tuition, fees and funding

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