Modelling and Simulation of Conservative Dynamical Systems by Computer Algebra Assisted Lagrangian Mechanics

Sammanfattning: Conservative dynamical systems is modelled with Lagrangian mechanics using Maple TM with the KTH developed plug-in symbolic package Sophia and simulated using Matlab®. Two double pendulum configurations and an object in a Keplerian orbit is studied. Motions and phase portraits are analysed, and numerical verifications of Kepler’s laws are performed. Properties concerning chaos is determined partly by examining sensitivity to initial conditions and it is shown that the 2D pendulum exhibits non-periodic behaviour whilst the 3D pendulum exhibits chaotic behaviour. Kepler’s laws are reproduced under certain assumptions. Finally, the applicability of Lagrangian mechanics when applied to conservative dynamical systems is evaluated.