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Analytical Mechanics

  • Number of credits 7.5 credits
  • Level Bachelor's level
  • Starting Spring Term 2022

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

Application and eligibility

Analytical Mechanics, 7.5 credits

Det finns inga tidigare terminer för kursen Spring Term 2022 Det finns inga senare terminer för kursen

The information below is only for exchange students

Starts

8 April 2022

Ends

5 June 2022

Study location

Umeå

Language

English

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.

Selection

Students applying for courses within a double degree exchange agreement, within the departments own agreements will be given first priority. Then will - in turn - candidates within the departments own agreements, faculty agreements, central exchange agreements and other departmental agreements be selected.

Application code

UMU-A5305

Application

This application round is only intended for nominated exchange students. Information about deadlines can be found in the e-mail instruction that nominated students receive. The application period is closed.

Contact us

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Contactperson for the course is:
Michael Bradley