The period function at a C 1 switching level: loss of smoothness and a critical period for a pendulum with unilateral elastic stops

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

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Publication Details

Journal
Research Square
Published
2026-11-05
DOI
https://doi.org/10.21203/rs.3.rs-11415393/v1
Primary Topic
Advanced Differential Equations and Dynamical Systems
Type
preprint
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preprint

The period function at a C 1 switching level: loss of smoothness and a critical period for a pendulum with unilateral elastic stops

Alvaro Humberto Salas
Research Square
Advanced Differential Equations and Dynamical Systems
preprint

The period function at a C 1 switching level: loss of smoothness and a critical period for a pendulum with unilateral elastic stops

Alvaro Humberto Salas
preprint en

Abstract

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

Research Square
Universidad Nacional de Colombia (CO)
Advanced Differential Equations and Dynamical Systems
DOIOpen Access PDFOpenAlex
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The period function at a C 1 switching level: loss of smoothness and a critical period for a pendulum with unilateral elastic stops — Alvaro Humberto Salas · Research Square (2026) | TGRS Research Map | TGRS