| Popis: |
This thesis gives a brief introduction to the Hamiltonian formalism and symplectic geometry. The Hamilton theory is applied on three systems - the pendulum, a parti- cle in a central potential field and rigid body rotation.The main focus of this thesis is to derive several symplectic integrators: the symplectic Euler schemes, Verlet schemes, implicit mid-point rule method and a parametric symplectic integrator. The symplectic integrators will be compared with each other and with two non-symplectic integrators - the explicit Euler scheme and the Ehrenfest integrator. For the comparison we will use harmonic oscillator, a particle in a central gravitational field and rigid body rotation. 1 |
