Resonance capture in a three degree-of-freedom mechanical system
The author studies the phenomena of resonance capture in a three degree-of freedom dynamical system modeling the dynamics of an unbalanced rotor, subject to a small constant torque, supported by orthogonal, linearly elastic supports, which is constrained to move in the plane. The equations of motion are: \(\ddot x+x=\varepsilon_1\dot\theta^2\cos\theta\), \(\ddot y+\mu^2y= \varepsilon_1 \dot \theta^2\sin\theta\), \(\ddot\theta= \varepsilon_2 \{\alpha+ [\mu^2y\cos\theta-x\sin \theta]\}\). Using the method of averaging and restricting the dynamics to a neighborhood of the resonance, the author develops a local system of equations which describes the essential dynamical behavior. These equations, locally valid near the resonance, possess a small parameter which is related to the imbalance. Using a generalized Melnikov integral, the author characterizes the splitting distance between the invariant manifolds which govern capture and escape from resonance.
scientific article; zbMATH DE number 1089286