Ramachandran, R.; Nosonovsky, M. “Kirchhoff’s Analogy between the Kapitza Pendulum Stability and Buckling of a Wavy Beam under Tensile Loading.” Appl. Mech. 2023, 4, 248-253. https://doi.org/10.3390/applmech4010014

Our paper is about a non-trivial analogy between the stabilization of an inverted pendulum on a vibrating foundation (i.e., in the temporal domain) and the buckling stability of a wavy rod (i.e., in the spatial domain). Dynamic equations of motion of a pendulum have the same structure as the differential equations governing the static deflection of an elastic beam (or rod), which is known as Kirchhoff’s analogy.