Analytical Mechanics and Field Theory (FYS500)

Content

Introduction to variational calculus and the Lagrange multiplier method. Hamilton’s variational principle and the Lagrange formulation of mechanics. Symmetries and conservation laws. Applications, including motion in central fields, dynamics of rigid bodies, oscillations, and the Lagrangian formulation of special relativity. Hamilton’s formulation of mechanics.

Continuous systems and fields, the Lagrange and Hamilton formulations of mechanics of continuous systems. Conservation laws for fields, the energy-momentum tensor. Overview of important classical field theories, Maxwell’s electrodynamics as a relativistic field theory.

Learning outcome

After completing the course, the student should:

K1: Have knowledge of the Lagrangian and Hamiltonian formulations of classical mechanics, and core applications of these formalisms.

K2: Have knowledge of relativistic mechanics and its range of validity.

K3: Have knowledge of classical field theory, including specific field theories that occur in our description of Nature.

F1: Be able to apply the Lagrangian and Hamiltonian formalism to moderately advanced mechanical systems, derive the equations of motion and solve them.

F2: Be able to analyse and solve classical mechanics problems involving rotating rigid bodies.

F3: Be able to analyse select central applications in detail using the Lagrangian formalism.

G1: Have an understanding of how the topics of the course (Lagrangian, Hamiltonian, relativistic, field theory mechanics) fit into and connect different areas of physics, including Newtonian mechanics, electromagnetism, quantum mechanics and field theory applications.

Required prerequisite knowledge

Recommended prerequisites

Exam

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Method of work

Open for

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Literature