The parametrically excited pendulum and the criteria for predicting the onset of chaos

A pendulum with its supporting point vibrating in both the x and the y direction is analyzed. Numerical simulation by computer is used to analyze the motion of the pendulum. Chaotic motion of the system is observed. Threshold values for chaos are obtained by simulation. The Lyapunov exponent and the fast Fourier transform ( FFT ) are used as the criteria to determine if the system is chaotic. Two predictive theoretical criteria, the Melnikov criterion and a period-doubling criterion, are then applied to the system. The results obtained by simulation and by theoretical criteria are shown to be in good agreement. A brute-force approach is used to supplement the results. It is found that the motion of this simple driven pendulum will have very complicated behavior. Multiple attractors can be shown to coexist.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Engineering Mechanics

Department dc:contributor.department

Engineering Mechanics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1991

Author dc:creator

• Hsu, Tseng-Hsing

Chair dc:contributor.committeechair

• Hendricks, Scott L.

Committee members dc:contributor.committeemember

• Smith, Charles W.
• Mook, Dean T.

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

etd-03242009-040616

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/41763