The period function at a C 1 switching level: loss of smoothness and a critical period for a pendulum with unilateral elastic stops
Year: 2026
Type: preprint
Abstract: We study the period function of planar conservative systems¨xsystems¨ systems¨x + W ′ (x) = 0 whose potential is C 1 but piecewise analytic, the switching being caused by a unilateral elastic constraint that engages at x = x g. If W ′ (x g) = d > 0 and W ′′ jumps by J at x g , we prove that the period satisfies T (h) = T (h) − 4
Source: Research Square
Author: Alvaro H. Salas
Institution: Universidad Nacional de Colombia
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225320900