Investigation into the Local and Global Bifurcations of the Whirling Planar Pendulum

This thesis details the investigation into the Whirling Planar Pendulum system. The WPP is a pendulum that is spun around a vertical spin axis at a controllable horizontal offset. This dynamical system exhibits both local and global bifurcations. The local pitchfork bifurcation leads to the splitting of a single stable equilibrium point into three (two stable and one unstable), as the spin rate is increased. The global bifurcations lead to two independent types of chaotic oscillations which are induced by sinusoidal excitations. The types of chaos are each associated with one of two homoclinic orbits in the system's phase portraits. The onset of each type of chaos is investigated through Melnikov's Method applied to the system's Hamiltonian, to find parameters at which the stable and unstable manifolds intersect transversely, indicating the onset of chaotic motion. These results are compared to simulation results, which suggest chaotic motion through the appearance of strange attractors in the Poincaré maps. Additionally, evidence of the WPP system experiencing both types of chaos simultaneously was found, resulting in a merger of two distinct types of strange attractor.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Aerospace Engineering

Department dc:contributor.department

Aerospace and Ocean Engineering

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2019

Author dc:creator

• Hyde, Griffin Nicholas

Chair dc:contributor.committeechair

• Woolsey, Craig A.

Committee members dc:contributor.committeemember

• Southward, Steve C.
• Philen, Michael K.

• Chaos theory
• Bifurcation theory
• Whirling Planar Pendulum

Statement dc:rights

• In Copyright

Licence dc:rights.uri

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

Dc Identifier Other

vt_gsexam:21395

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/91395