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Updated: Dec 31, 2025

Magnetically Induced Rotating Rayleigh-Taylor Instability
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Classical three rotor problem: Periodic solutions, stability and chaos.

Govind S Krishnaswami1, Himalaya Senapati1

  • 1Physics Department, Chennai Mathematical Institute, SIPCOT IT Park, Siruseri, Chennai 603103, India.

Chaos (Woodbury, N.Y.)
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Summary
This summary is machine-generated.

This study explores the dynamics of three coupled rotors, revealing an order-chaos-order behavior. The system transitions from regular to chaotic motion as energy increases, with periodic solutions found at various energy levels.

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Area of Science:

  • Classical mechanics
  • Dynamical systems theory
  • Nonlinear dynamics

Background:

  • Investigates the classical dynamics of three coupled rotors with attractive cosine potentials.
  • This system models coupled Josephson junctions in its classical limit.
  • Energy (E) is the sole free parameter governing the relative motion.

Purpose of the Study:

  • To identify periodic solutions within the three-rotor system.
  • To characterize the transition from regular to chaotic dynamics.
  • To analyze the impact of energy on system stability and symmetry.

Main Methods:

  • Analysis of periodic solutions, including pendulum, isosceles, and choreographies.
  • Examination of Poincaré surfaces to identify chaotic regions and symmetry breaking.
  • Application of the Jacobi-Maupertuis metric to assess curvature and chaos.

Main Results:

  • Families of periodic solutions (pendulum, isosceles, choreographies) exist across different energy levels.
  • The system exhibits an order-chaos-order behavior, transitioning to chaos around E≈4.
  • Pendulum solutions exhibit alternating stability, and discrete symmetries break during the transition to chaos.

Conclusions:

  • The three-rotor system demonstrates complex dynamics with a clear transition to chaos.
  • Energy level is critical in determining the system's regularity, chaoticity, and stability.
  • The findings offer insights into nonlinear dynamics and the behavior of coupled systems.