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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Isochronicity of a class of piecewise continuous oscillators


Authors: Francesc Mañosas and Pedro J. Torres
Journal: Proc. Amer. Math. Soc. 133 (2005), 3027-3035
MSC (2000): Primary 34C05, 34C15
Published electronically: March 31, 2005
MathSciNet review: 2159782
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Abstract: Motivated by a classical pendulum clock model suggested by Andrade in 1920, we study the equation $\ddot x+g(x)\mathop{sgn}\nolimits{\dot x}+x=0$ and prove that for a nonlinear analytic $g$ the origin is never an isochronous focus or an isochronous center.


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Additional Information

Francesc Mañosas
Affiliation: Departament de Matematiques, Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
Email: Francesc.Manosas@uab.es

Pedro J. Torres
Affiliation: Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain
Email: ptorres@ugr.es

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07873-1
PII: S 0002-9939(05)07873-1
Keywords: Isochronous, center, focus
Received by editor(s): March 1, 2004
Received by editor(s) in revised form: May 27, 2004
Published electronically: March 31, 2005
Additional Notes: The first author was partially supported by DGES No. BFM2002-04236-C02-2, BFM2002-01344 and the CONACIT grant number 2001SGR-00173.
The second author was partially supported by D.G.I. BFM2002-01308, Ministerio Ciencia y Tecnología, Spain
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2005 American Mathematical Society