On the global geometric structure of the dynamics of the elastic pendulum
The authors studies the dynamics of planar elastic pendulum by considering it as a singular perturbation of uncoupled pendulum. The equations of motion are \(\ddot\theta+ {2\dot\theta \dot R\over 1+R}+ {\sin\theta \over 1+R}=0\) and \(\ddot R+({\omega_s \over\omega_p})^2 R-(1+R_)\dot \theta^2+1-\cos\theta=0\), where \(\omega_p\) and \(\omega_s\) denote respectively natural frequencies of the pendulum and radial oscillator. The author determines the global geometric structure of the dynamics in terms of two-dimensional invariant manifolds of motion. A general analytic study is carried out and confirmed by numerical experiments.
two-dimensional invariant manifolds of motion
scientific article; zbMATH DE number 1342560