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Motion of a parametrically driven damped coplanar double pendulum.

Rebeka Sarkar1, Krishna Kumar1, Sugata Pratik Khastgir1

  • 1Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur-721302, West Bengal, India.

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Summary
This summary is machine-generated.

We studied the stability and motion of a damped double pendulum vibrated vertically. Parametric driving can stabilize inverted states, leading to periodic or chaotic dynamics.

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Area of Science:

  • Physics
  • Mechanical Engineering
  • Nonlinear Dynamics

Background:

  • The behavior of driven pendulums is a classic problem in physics.
  • Understanding the stability and dynamics of double pendulums is crucial for various mechanical systems.

Purpose of the Study:

  • To analyze the linear stability and nonlinear motion of a damped coplanar double pendulum subjected to vertical sinusoidal vibration.
  • To investigate the influence of driving parameters (amplitude and frequency) on the pendulum's stability and motion.

Main Methods:

  • Calculation of Floquet multipliers for different driving parameters.
  • Analysis of stationary states, including downward and upward configurations.
  • Examination of velocity-dependent damping and a wide range of driving frequencies.

Main Results:

  • The double pendulum exhibits both periodic (oscillatory, rotational, harmonic, subharmonic) and chaotic motion.
  • For equal masses, limit cycles in configuration space are linear.
  • For unequal masses, multi-period, chaotic, or rotational swings are observed depending on amplitude and damping.

Conclusions:

  • Parametric driving can stabilize partially or fully inverted double pendulum states.
  • The system's behavior is rich, displaying complex dynamics including chaos.
  • The study provides insights into the control and stabilization of complex mechanical oscillators.