Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 31, Issue 5, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127421500759
Keywords
KCC-theory; Jacobi stability; deviation; chaos; mechanical system
Funding
- National Natural Science Foundation of China [11772306]
- Zhejiang Provincial Natural Science Foundation of China [LY20A020001]
- Fundamental Research Funds for the Central Universities, China University of Geosciences [CUGGC05]
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In this paper, the Jacobi stability of a two-degree-of-freedom mechanical system is investigated using differential geometric methods. The construction of geometric invariants allows for a discussion on the stability of two equilibria and a periodic orbit. The phase portraits of deviation vectors near equilibria, along with the sensitivity of these vectors to initial conditions, are illustrated to predict chaos onset quantitatively.
In this paper, the Jacobi stability of a two-degree-of-freedom mechanical system is studied by the innovative application of KCC-theory, namely differential geometric methods. We discuss the Jacobi stability of two equilibria and a periodic orbit by constructing geometric invariants. Both the regions of Jacobi stability and Lyapunov stability are presented to show the difference. We draw the phase portraits of the deviation vector near two equilibria under specific parameter values and initial conditions, and point out the sensitivity of deviation vector to initial conditions. In addition, the corresponding instability exponent and curvature are applicable for predicting the onset of chaos, which help us to detect chaotic behaviors quantitatively.
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