Circular Landau oscillator
$$U(\theta)=\frac{\alpha\omega_1^2}\lambda\cos\theta-\beta\omega_1^2\sqrt{1+\alpha^2+2\alpha\cos\theta}$$ The graphs below show the phase space, potential, and a physical representation of the pendulum in motion. The energy and the parameter $\beta$ can be adjusted with the sliders below and exhibit the different types of motion:
- Gravitational regime: $\beta >(1+\alpha)/\lambda$
- Intermediate regime: $\beta\in((1-\alpha)/\lambda,(1+\alpha)/\lambda)$
- Spring regime: $\beta<(1-\alpha)/\lambda$
| Energy: | $E=$-0.5 |
| Beta: | $\beta=$-0.5 |