Rocking motion of an optical wing: theory.

The intensity-dependent rocking frequency of an illuminated semicylindrical refractive rod (or "optical wing") on a flat, nonslip surface is investigated. Both longitudinal and transverse radiation pressure forces (scatter and lift forces), as well as radiation pressure torque, transform the mechanical system into one having a bistable potential energy above a critical intensity. The equation of motion may be written as a parametrically driven nonlinear bistable harmonic oscillator, resulting in complex rocking dynamics. The effects of linear and sinusoidal intensity modulation schemes are explored, and experimental conditions to verify these results are discussed.

A five-link 2D brachiating ape model with life-like zero-energy-cost motions.

We have found periodic life-like brachiating motions of a rigid-body ape model that use no muscle or gravitational energy to move steadily forward. The most complicated of these models has 5 links (a body and two arms, each with 2 links) and 7 degrees of freedom in flight. The defining feature of all our periodic solutions is that all collisions are at zero relative velocity. These motions are found using numerical integration and root-finding that is sufficiently precise so as to imply that the solutions found correspond to mathematical solutions with exactly zero energy cost. The only actuation and control in the model is for maintaining contact with and releasing handholds which requires no mechanical work. The similarity of these energy-free simulations to the motions of apes suggests that muscle-use minimization at least partially characterizes the coordination strategies they use.