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Escape from a potential well under aperiodic forcing and damping with application to ship capsize
Alex McSweeney-Davis1, R S MacKay1, Shibabrat Naik1
1Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom.
Chaos (Woodbury, N.Y.)
|July 9, 2025
Summary
Researchers computationally identified normally hyperbolic submanifolds (NHS) in a ship motion model. This method classifies initial ship states as safe or unsafe, crucial for understanding escape dynamics.
Area of Science:
- Physics
- Mechanical Engineering
- Naval Architecture
Background:
- Escape dynamics from potential wells are prevalent across physical systems, including chemical reactions and maritime safety.
- Normally hyperbolic submanifolds (NHS) are key structures governing escape trajectories in dynamical systems.
- Understanding these dynamics is critical for predicting system behavior, such as ship stability.
Purpose of the Study:
- To computationally implement an algorithm for identifying normally hyperbolic submanifolds (NHS) in a two-degrees-of-freedom ship motion model.
- To investigate the influence of damping and aperiodic forcing on escape dynamics.
- To utilize the stable manifolds of NHS for classifying initial ship states.
Main Methods:
- Development and application of a computational algorithm to locate NHS in a reduced ship dynamics model.
- Analysis of a two-degrees-of-freedom system incorporating damping and external forcing.
- Utilizing stable manifold theory to differentiate between safe and unsafe initial conditions.
Main Results:
- Successful identification of the normally hyperbolic submanifolds (NHS) within the specified ship motion model.
- Demonstration that the stable manifolds of these NHS can effectively distinguish between safe and unsafe initial ship states.
- Quantification of the impact of damping and forcing on the geometry of NHS and associated manifolds.
Conclusions:
- The computational method provides a robust framework for analyzing escape dynamics in complex systems like ship motion.
- Stable manifold analysis of NHS offers a powerful tool for real-time risk assessment and state classification in maritime safety.
- This approach enhances the understanding of nonlinear dynamics and its application to critical engineering problems.
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