Jacobi stability for dynamical systems of two-dimensional second-order differential equations and application to overhead crane system

DOI10.1142/S0219887816500456zbMath1344.37089WikidataQ115245378 ScholiaQ115245378MaRDI QIDQ2805565

Takahiro Yajima, Kazuhito Yamasaki

Publication date: 12 May 2016

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

zbMATH Keywords

Hopf bifurcationJacobi stabilityoverhead crane system

Mathematics Subject Classification ID

Stability for nonlinear problems in mechanics (70K20) Control of mechanical systems (70Q05) Stability of solutions to ordinary differential equations (34D20) Dynamical systems in classical and celestial mechanics (37N05) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25)

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Cites Work

• Jacobi stability analysis of dynamical systems - applications in gravitation and cosmology
• The theory of sprays and Finsler spaces with applications in physics and biology
• Nonlinear control of engineering systems. A Lyapunov-based approach.
• Parallelism and path-spaces
• Observations sur le memoire precedent
• Finslerian Volterra-Hamilton systems in Clementsian forest succession
• Nonlinear Stability Analysis of the Emden–Fowler Equation
• A Transient-State Analysis of Tyson's Model for the Cell Division Cycle by Means of KCC-Theory
• KCC-theory and geometry of the Rikitake system
• Jacobi stability analysis of the Lorenz system
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