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On the Stable Limit Cycle of a Weight-Driven Pendulum Clock

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Title: On the Stable Limit Cycle of a Weight-Driven Pendulum Clock
Language: English
Authors: Llibre, J, Teixeira, M. A.
Source: European Journal of Physics. Sep 2010 31(5):1249-1254.
Availability: Institute of Physics Publishing. The Public Ledger Building Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106. Tel: 215-627-0880; Fax: 215-627-0879; e-mail: info@ioppubusa.com; Web site: http://www.iop.org/EJ/journal/EJP
Peer Reviewed: Y
Physical Description: PDF
Page Count: 6
Publication Date: 2010
Document Type: Journal Articles
Reports - Descriptive
Education Level: Higher Education
Descriptors: Calculus, Motion, Physics, Scientific Principles, Science Instruction, Graduate Study, College Science, Problem Solving, Validity, Theories, Equations (Mathematics)
DOI: 10.1088/0143-0807/31/5/024
ISSN: 0143-0807
Abstract: In a recent paper (Denny 2002 Eur. J. Phys. 23 449-58), entitled "The pendulum clock: a venerable dynamical system", Denny showed that in a first approximation the steady-state motion of a weight-driven pendulum clock is shown to be a stable limit cycle. He placed the problem in a historical context and obtained an approximate solution using the Green function. In this paper we obtain the same result with an alternative proof via known issues of classical averaging theory. This theory provides a useful means to study a planar differential equation derived from the pendulum clock, accessible to Master and PhD students. (Contains 1 figure.)
Abstractor: As Provided
Number of References: 9
Entry Date: 2010
Accession Number: EJ901541
Database: ERIC
FullText Text:
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  Data: In a recent paper (Denny 2002 Eur. J. Phys. 23 449-58), entitled "The pendulum clock: a venerable dynamical system", Denny showed that in a first approximation the steady-state motion of a weight-driven pendulum clock is shown to be a stable limit cycle. He placed the problem in a historical context and obtained an approximate solution using the Green function. In this paper we obtain the same result with an alternative proof via known issues of classical averaging theory. This theory provides a useful means to study a planar differential equation derived from the pendulum clock, accessible to Master and PhD students. (Contains 1 figure.)
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