Accurate natural frequency estimation for the double pendulum

Determine accurate values of the natural frequencies associated with the two coupled oscillatory modes of the double pendulum by linearizing the learned neural state vector field at the identified stable equilibrium and extracting eigenvalues of its Jacobian, using only video recordings as input and accounting for the interaction between the two modes.

Background

The paper introduces a method that learns smooth neural state variables and a corresponding neural state vector field directly from videos, enabling analyses common in dynamical systems, such as equilibrium identification and linearization. For the spring mass and single pendulum systems, the authors successfully estimate natural frequencies from the Jacobian of the learned vector field near stable equilibria.

In contrast, for the double pendulum, which possesses two interacting oscillatory modes, the authors state they were unable to obtain accurate frequency estimates. This highlights an unresolved challenge in extracting the characteristic frequencies from the learned representation when multiple coupled modes are present.