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- Title
Subharmonic Bifurcation for a Non-smooth Double Pendulum with Unilateral Impact.
- Authors
Xiu-ying Guo; Gang Zhang; Rui-lan Tian
- Abstract
A unilateral impact double pendulum model with hinge links is constructed to detect subharmonic bifurcation for the high dimensional non-smooth system. The non-smooth and nonlinear coupled factors lead a barrier for high dimensional conventional nonlinear techniques. By introducing reversible transformation and energy time scale transformation, the system is expressed as a smooth decoupling form of energy coordinates. Thus, the concept of subharmonic Melnikov function is extended to high-dimensional nonsmooth systems, and the influence of impact recovery coefficient on the existence of subharmonic periodic orbits of double pendulum is revealed. The efficiency of the theoretical results is verified by phase portraits, time process portraits and Poincaré section.
- Subjects
DOUBLE pendulums; SUBHARMONIC functions; MATHEMATICAL decoupling; POINCARE conjecture; PENDULUMS
- Publication
Journal of Nonlinear Mathematical Physics, 2022, Vol 29, Issue 2, p349
- ISSN
1402-9251
- Publication type
Article
- DOI
10.1007/s44198-022-00039-8