TRA CỨU
thông tin biểu ghi
ISBN 9789813231672
DDC 531.45
Tác giả CN Luo, Albert C. J.
Nhan đề Resonance and bifurcation to chaos in pendulum / Albert C. J. Luo
Thông tin xuất bản Beijing : World Scientific, 2018
Mô tả vật lý xii, 238 page. ; 24 cm.
Tóm tắt A periodically forced mathematical pendulum is one of the typical and popular nonlinear oscillators that possess complex and rich dynamical behaviors. Although the pendulum is one of the simplest nonlinear oscillators, yet, until now, we are still not able to undertake a systematical study of periodic motions to chaos in such a simplest system due to lack of suitable mathematical methods and computational tools. To understand periodic motions and chaos in the periodically forced pendulum, the perturbation method has been adopted. One could use the Taylor series to expend the sinusoidal function to the polynomial nonlinear terms, followed by traditional perturbation methods to obtain the periodic motions of the approximated differential system. This book discusses Hamiltonian chaos and periodic motions to chaos in pendulums. This book first detects and discovers chaos in resonant layers and bifurcation trees of periodic motions to chaos in pendulum in the comprehensive fashion, which is a base to understand the behaviors of nonlinear dynamical systems, as a results of Hamiltonian chaos in the resonant layers and bifurcation trees of periodic motions to chaos. The bifurcation trees of travelable and non-travelable periodic motions to chaos will be presented through the periodically forced pendulum.
Từ khóa tự do Nonlinear oscillations
Từ khóa tự do Chaos theory
Từ khóa tự do Bifurcation
Từ khóa tự do Pendulum dynamics
Từ khóa tự do Resonance
Từ khóa tự do Mathematical modeling
Từ khóa tự do Dynamical systems
Địa chỉ 300Q12_Kho Mượn_02(2): 100506-7
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082 |a531.45|bL964|223
100 |aLuo, Albert C. J.
245 |aResonance and bifurcation to chaos in pendulum / |cAlbert C. J. Luo
260 |aBeijing : |bWorld Scientific, |c2018
300 |axii, 238 page. ; |c24 cm.
520 |aA periodically forced mathematical pendulum is one of the typical and popular nonlinear oscillators that possess complex and rich dynamical behaviors. Although the pendulum is one of the simplest nonlinear oscillators, yet, until now, we are still not able to undertake a systematical study of periodic motions to chaos in such a simplest system due to lack of suitable mathematical methods and computational tools. To understand periodic motions and chaos in the periodically forced pendulum, the perturbation method has been adopted. One could use the Taylor series to expend the sinusoidal function to the polynomial nonlinear terms, followed by traditional perturbation methods to obtain the periodic motions of the approximated differential system. This book discusses Hamiltonian chaos and periodic motions to chaos in pendulums. This book first detects and discovers chaos in resonant layers and bifurcation trees of periodic motions to chaos in pendulum in the comprehensive fashion, which is a base to understand the behaviors of nonlinear dynamical systems, as a results of Hamiltonian chaos in the resonant layers and bifurcation trees of periodic motions to chaos. The bifurcation trees of travelable and non-travelable periodic motions to chaos will be presented through the periodically forced pendulum.
541 |aTặng
653 |aNonlinear oscillations
653 |aChaos theory
653 |aBifurcation
653 |aPendulum dynamics
653 |aResonance
653|aMathematical modeling
653|aDynamical systems
852|a300|bQ12_Kho Mượn_02|j(2): 100506-7
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