Analytical Mechanics
Tampere University
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.
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