Classical Mechanics

Constraints and generalized coordinates. Virtual displacements, Lagrange's equations. Variational calculus, Hamilton's principle. Lagrangian for a particle in an electromagnetic field. Constants of motion, symmetry properties. Virial theorem. Central forces. Elements of the kinematics and dynamics of rigid bodies. Special relativity. Normal coordinates. Hamilton's equations. Canonical transformations.

Knowledge:

• Understanding the physical principle behind the derivation of Lagrange's and Hamilton's equations, and the advantages of these formulations.
• Being able to relate symmetries to conservation laws in physical systems, and apply these concepts to practical situations.
• Being familiar with the fundamental principles of the special theory of relativity.
• Understanding the intricacies of moving-reference frames and rigid-body motion.

Skills:

• Analytic solving of differential equations of mechanical systems (equations of motion).
• Applying linear transformations for rotations, coupled differential equations and Lorentz transformations.
• Special techniques in Hamiltonian dynamics (Poisson brackets, generating functions).
• Applying computational (numerical) methods for solving mechanical problems.

General competence:

• Master different problem-solving strategies within mechanical physics and assess which of these strategies is most useful for a given problem.
• Understanding the contribution of the Lagrangian/Hamiltonian formulation of classical physics in statistical physics, electromagnetism, and quantum mechanics.

Lectures and compulsory exercises. Computational physics components may be included in the lectures and the homework assignments. Expected workload in the course is 225 hours.