Multiplicity of forced oscillations for the spherical pendulum acted on by a retarded periodic force. (March 2017)

• Record Type: Journal Article
• Authors: Calamai, Alessandro; Pera, Maria Patrizia; Spadini, Marco
• Is Part Of: Nonlinear analysis. Volume 151(2017)
• Page Start: 252
• Page End: 264
• Publication Date: 2017-03
• Subjects: 34C25 -- 34K13 -- 70K40 -- 34C40; Retarded functional differential equations -- Multiplicity of periodic solutions -- Forced motion on manifolds -- Degree of a tangent vector field; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.12.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove a multiplicity result for forced oscillations of a spherical pendulum (that is, a massive point moving on a sphere) subject to a periodic action, with or without friction, allowed to depend on the whole past of the motion. The approach is based on topological methods. In particular, when the unperturbed forcing term is the gravity, we obtain two harmonic forced oscillations regardless of the presence of friction and of the form of the perturbing force field.