- L.N. Virgin and L.A. Cartee, Note on the escape from a potential well,
International Journal of Non-Linear Mechanics, vol. 26 no. 3-4
pp. 449 - 452 [0020-7462(91)90074-4] .
(last updated on 2010/12/05)
This brief note compares analytical results pertaining to the escape from a potential well. The system studied is the classical Duffing's equation with positive linear and negative cubic stiffness terms, i.e. a softening spring characteristic. Under gradually increasing periodic forcing, close to resonance, solutions may escape from the potential in which the system is oscillating. Comparison is made between the method of multiple scales and the harmonic balance method, and their stability characteristics investigated using Floquet theory and the Routh-Hurwitz criterion. This type of equation is familiar as an approximation to the motion of a pendulum, and similar types of equations have more recently been used to model the roll response of floating vessels in regular waves.