Numerical Approach of Hamilton Equations on Double Pendulum Motion with Axial Forcing Constraint

Abstract

Double pendulum with axial forcing constraint is considered by using Hamilton equations. In this case, the total Hamiltonian is complicated because of its constraint. There is additional terms which is add to the usual Hamiltonian. Four equations of motion is obtained from the Hamilton equations since the degree of freedom is four. Solutions of the equations are solved numerically by Runge-Kutta method. The results are plotted in poincare maps. In this case, the maps is displayed in various initial value. The chaotic behavior can be indicated which depends on given time function forcing constraint.