Researchers show that a small, controlled pendulum machine can move energy into an oscillation that lives only in the lower arms. The device is a branched double pendulum: one “parent” link at the top and two identical “child” links below. When the children swing together (in-phase), a different motion — the antiphase mode, in which the two children swing opposite each other — is not excited at the start. The team found that, if the parent starts with a large enough angle, nonlinear motion can drive energy into that antiphase mode and make it grow.

The experiment was designed so the antiphase motion is localized to the child links. That localization makes it easy to prepare the initial state: the parent is pulled aside and released while the two children are held vertical, so only the in-phase motions are present initially. The authors treat the pendulum as a Hamiltonian mechanical system (energy-conserving equations) and derive a formula for the instantaneous rate of energy flow into the antiphase mode. They use a Poisson bracket, a standard mathematical operation in Hamiltonian mechanics, to turn the Hamiltonian into a compact energy-transfer function.

Because exact formulas are messy, the theory uses controlled approximations. The mass matrix simplifies when the two child links are equal and when a small coupling parameter is small; the authors keep first-order corrections and use a potential energy form that remains meaningful for finite angles. From this approximated Hamiltonian they separate a sub-Hamiltonian that describes the antiphase degree of freedom and identify two contributions to the transfer: one coming from kinetic coupling and one from the potential terms.

They tested the theory on a real acrylic pendulum whose motion was recorded with a Canon EOS Kiss M camera. Each link carried two colored dot stickers and the team used video tracking to extract time series of the angles. From small-amplitude trials they identified three eigenfrequencies near 0.88 Hz, 1.26 Hz and 1.58 Hz and used those values to fix the moments of inertia (I1 ≈ 1.88×10^-3 and I2 ≈ 0.516×10^-3 in the paper). In energy-transfer trials the parent was released from several initial angles after the children were allowed to settle; the data showed that the antiphase variable grows when the parent angle is sufficiently large. The authors compute the transfer function from the measured time series and use it to detect the inflow of energy into the antiphase mode.