Continuation of Periodic Solutions of Dissipative and Conservative Systems : Application to Elastic Pendulum
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-06-02
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
Continuation is an efficient algorithm for finding solutions of systems of nonlinear algebraic equations where the solutions form a one-dimensional continuum.
Such systems arise naturally when investigating equilibrium points and periodic solutions of ordinary differential equations with one parameter.
Continuation of isolated periodic solutions of dissipative systems is a well-established technique.
Less attention has been devoted to continuation of periodic solutions of conservative systems, where periodic solutions typically form a one-parameter family.
To specify a single periodic solution, additional condition must be considered.
However, this gives an over-determined system, which has no solution when working with approximate numerical values.
We propose a simple algorithm which solves this difficulty by using singular value decomposition of the Jacobian matrix.
This algorithm is applied to the conservative model of elastic pendulum.
A branch of periodic solutions with constant energy is found which is born by the period doubling bifurcation of vertical oscillations.
American Psychological Association (APA)
Pokorny, P.. 2009. Continuation of Periodic Solutions of Dissipative and Conservative Systems : Application to Elastic Pendulum. Mathematical Problems in Engineering،Vol. 2009, no. 2009, pp.1-15.
https://search.emarefa.net/detail/BIM-446688
Modern Language Association (MLA)
Pokorny, P.. Continuation of Periodic Solutions of Dissipative and Conservative Systems : Application to Elastic Pendulum. Mathematical Problems in Engineering No. 2009 (2009), pp.1-15.
https://search.emarefa.net/detail/BIM-446688
American Medical Association (AMA)
Pokorny, P.. Continuation of Periodic Solutions of Dissipative and Conservative Systems : Application to Elastic Pendulum. Mathematical Problems in Engineering. 2009. Vol. 2009, no. 2009, pp.1-15.
https://search.emarefa.net/detail/BIM-446688
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-446688