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Optimal dynamical stabilization.

Arnaud Lazarus1, Emmanuel Trélat2

  • 1Massachusetts Institute of Technology, Sorbonne Université, CNRS, Institut Jean Le Rond d'Alembert, UMR7190, Paris, France and , Department of Mathematics, Cambridge, Massachusetts 02139, USA.

Physical Review. E
|April 18, 2026
PubMed
Summary
This summary is machine-generated.

New minimal stability conditions, termed optimal dynamical stabilization, were found for systems with periodically varying potential energy. This extends Kapitza stabilization and offers new passive stabilization techniques.

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Area of Science:

  • Physics
  • Dynamical Systems
  • Control Theory

Background:

  • Dynamical stability ensures bounded system responses to disturbances.
  • Classical criteria like Lyapunov and Kapitza stability are crucial in physics and technology.
  • Understanding minimal stability conditions is key for system design.

Purpose of the Study:

  • To establish new minimal conditions for dynamical stability in systems with time-varying potential energy.
  • To extend the concept of Kapitza stabilization to 'optimal dynamical stabilization'.
  • To determine the minimal time-periodic stiffness for stabilizing a linear mass-spring system.

Main Methods:

  • Utilizing optimal control theory to find minimal stabilization parameters.
  • Applying mathematical analysis to systems with periodically alternating potential energy curvature.
  • Validating theoretical predictions through model experiments.

Main Results:

  • Identified new minimal conditions for dynamical stability in periodically modulated systems.
  • Determined the minimal time-periodic stiffness for a linear mass-spring system.
  • Found that alternating potential curvature leads to discrete modulation functions governed by eigenvalue problems analogous to quantum mechanics.

Conclusions:

  • The study introduces 'optimal dynamical stabilization' for systems with time-varying potential energy.
  • Findings provide a deeper understanding of dynamical systems and their stability.
  • The research lays groundwork for novel passive stabilization techniques in applied physics.