Analytical Mechanics, 5 op

Core content

• Equations of motion and conservation laws. The two complementary approaches in mechanics: direct solution of time dependencies and first integrals from conserving quantities.
  
• Lagrangian and Hamiltonian methods in physics and variational approaches. Several applications, such as equations of motion in rotating coordinate system, charged particle in electromagnetic field, rigid body motion.
  
• Nonlinearity and chaos. Attractors, limit cycles, Hopf Bifurcations.
  
• Numerical solutions of equations of motion derived using Lagrangian and Hamiltonian methods. Molecular dynamics method.

Complementary knowledge

• Formulation and solution of field equations using variational methods. Correspondencies between classical and quantum mechanics.
• Stability considerations. Numerical solution of chaotic systems and Poincare maps.