Technicka 5, Prague 6, Czech Republic
Department of Mathematics, Prague Institute of Chemical Technology
Stability Condition for Vertical Oscillation of 3-dim Heavy Spring Elastic Pendulum
2008, vol. 13, no. 3, pp. 155-165
Equations of motion for 3-dim heavy spring elastic pendulum are derived and rescaled to contain a single parameter. Condition for the stability of vertical large amplitude oscillations is derived analytically relating the parameter of the system and the amplitude of the vertical oscillation. Numerical continuation is used to find the border of the stability region in parameter space with high precision. The stability condition is approximated by a simple formula valid for a large range of the parameter and of the amplitude of oscillation. The bifurcation responsible for the loss of stability is identified.