  We introduce a method for constructing reduced-order models directly from
videos of dynamical systems. The method uses a non-intrusive tracking to
isolate the motion of a user-selected part in the video of an autonomous
dynamical system. In the space of delayed observations of this motion, we
reconstruct a low-dimensional attracting spectral submanifold (SSM) whose
internal dynamics serves as a mathematically justified reduced-order model for
nearby motions of the full system. We obtain this model in a simple polynomial
form that allows explicit identification of important physical system
parameters, such as natural frequencies, linear and nonlinear damping and
nonlinear stiffness. Beyond faithfully reproducing attracting steady states and
limit cycles, our SSM-reduced models can also uncover hidden motion not seen in
the video, such as unstable fixed points and unstable limit cycles forming
basin boundaries. We demonstrate all these features on experimental videos of
five physical systems: a double pendulum, an inverted flag in counter-flow,
water sloshing in tank, a wing exhibiting aeroelastic flutter and a shimmying
wheel.
