Extreme rotational events in a forced-damped nonlinear pendulum

Area of Science:

• Physics
• Nonlinear Dynamics
• Mathematical Modeling

Background:

• The pendulum is a fundamental system for studying oscillatory dynamics, bifurcations, and chaos.
• Understanding pendulum behavior is crucial for various physical phenomena reducible to its equations.

Purpose of the Study:

• To investigate the rotational dynamics of a two-dimensional forced-damped pendulum under AC and DC torque.
• To identify conditions leading to intermittent extreme rotational events and analyze their statistical properties.

Main Methods:

• Numerical simulations of the forced-damped pendulum equations.
• Analysis of angular velocity, return intervals, chaotic attractors, and phase slips.
• Investigation across a range of pendulum lengths and torque parameters.

Main Results:

• A specific pendulum length range was identified exhibiting intermittent extreme rotational events.
• Return intervals between extreme events follow an exponential distribution.
• Sudden increase in chaotic attractor size due to interior crisis triggers large amplitude events.
• Phase slips occur concurrently with extreme rotational events.

Conclusions:

• The study reveals unique rotational behaviors in forced-damped pendulums, including extreme events and phase slips.
• Chaotic dynamics, particularly interior crisis, are key drivers of instability and extreme events.
• Pendulum length and torque parameters critically influence the system's dynamics and the occurrence of these phenomena.