Kinematic asymmetries and the control of Lagrangian systems with oscillatory inputs

Some curvature-like geometric invariants of controlled Lagrangian systems are defined and shown to be of interest in determining the systems' response to high-frequency oscillatory inputs. The theory is illustrated by several examples of controlled rotating systems. For a rotating two d.o.f. pendulum with unequal cross-sectional moments of inertia, it is shown that a small-amplitude high-frequency oscillatory component of the rotational velocity can stabilize the neutral (hanging) equilibrium at average rates of rotation higher than the critical rate at which the neutral equilibrium loses stability for constant-velocity rotations. This and other examples illustrate the ways in which geometric and mechanical asymmetries affect a system's response to oscillatory forcing. Copyright (C) 2000 IFAC.