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arXiv Machine Learning By Leo Yao, Ziming Liu, Max Tegmark

Variational Continuation for Double Pendulum Periodic Orbits

Read the original on arXiv Machine Learning →

The paper introduces a Hessian‑based, integrator‑free method for numerically continuing periodic orbits in dynamical systems, using a Fourier series representation and automatic differentiation to avoid hand‑derived Jacobians. By exploiting flat directions in the loss landscape, the approach efficiently guides the search for periodic orbits, accurately initializes oscillations around unstable fixed points, and detects orbit family intersections and subharmonic bifurcations. Demonstrated on the double pendulum, the method produces full continuations from fixed points, revealing bifurcations along orbit families and identifying previously undocumented periodic orbits where both pendulum masses are never simultaneously at rest.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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