Analytical Mechanics

About this programme

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 t