Comparative lagrangian formulations for localized buckling

An energy functional for a strut on a nonlinear softening foundation is worked into two different lagrangian forms, in fast and slow space respectively. The developments originate independently of the underlying differential equation, and carry some quite general features. In each case, the kinetic energy is an indefinite quadratic form. In fast space, this leads to an escape phenomenon with fractal properties. In slow space, kinetic energy is added to a potential contribution that is familiar from modal formulations. Together, and in conjunction with a recent set of numerical experiments, they illustrate the extra complexities of localized, as opposed to distributed periodic, buckling.

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