单摆：共振层、分岔树到混沌（英文版）
定价：￥139.00
作者： 罗朝俊
出版社：高等教育出版社
- 高等教育出版社
- 9787040480047
- 1版
- 47266125-5
- 16开
- 290
- 理学
- 数学类
- 数学类
- 本科 研究生及以上
目录
目录
前辅文
1 Resonance and Hamiltonian Chaos
1.1 Stochastic layers
1.1.1 Definitions
1.1.2 Approximate criteria
1.2 Resonant separatrix layers
1.2.1 Layer dynamics
1.2.2 Approximate criteria
References
2 Hamiltonian Chaos in Pendulum
2.1 Resonance conditions
2.1.1 Conservative system
2.1.2 Resonance and energy increments
2.2 Stochastic layers
2.3 Resonant layers
2.3.1 Librational resonant layers
2.3.2 Rotational resonant layers
2.4 Numerical simulations
References
3 Parametric Chaos in Pendulum
3.1 Resonance and energy increment
3.1.1 Libration
3.1.2 Rotation
3.2 Parametric stochastic layers
3.2.1 Analytic predictions
3.2.2 Numerical predictions
3.2.3 Illustrations
3.2.4 Numerical simulations
3.3 Parametric resonant layers
3.3.1 Approximate predictions
3.3.2 Numerical illustrations
References
4 Nonlinear Discrete Systems
4.1 Definitions
4.2 Fixed points and stability
4.3 Stability switching theory
4.4 Bifurcation theory
References
5 Periodic Flows in Continuous Systems
5.1 Discretization-based methods
5.2 Discrete Fourier series
References
6 Periodic Motions to Chaos in Pendulum
6.1 Periodic motions in pendulum
6.1.1 Implicit discretization
6.1.2 Periodic motions
6.2 Bifurcation trees to chaos
6.2.1 Period-1 motions to chaos
6.2.2 Period-3 motions to chaos
6.2.3 Period-5 motions to chaos
6.3 Frequency-amplitude characteristics
6.3.1 Period-1 to period-4 motions
6.3.2 Period-3 to period-6 motions
6.3.3 Symmetric to asymmetric period-5 motions
6.4 Bifurcation trees varying with excitation amplitude
6.4.1 Non-travelable period-1 motions to chaos
6.4.2 Non-travelable period-3 motions to chaos
6.4.3 Travelable period-1 motions to chaos
6.4.4 Travelable period-2 motions to chaos
6.5 Numerical simulations
6.5.1 Non-travelable periodic motions
6.5.1.1 Period-1 to period-4 motions
6.5.1.2 Period-3 to period-6 motions
6.5.1.3 Period-5 motions
6.5.2 Travelable periodic motions
6.5.2.1 Travelable period-1 to period-2 motions
6.5.2.2 Travelable period-2 to period-8 motions
References
Subject Index
前辅文
1 Resonance and Hamiltonian Chaos
1.1 Stochastic layers
1.1.1 Definitions
1.1.2 Approximate criteria
1.2 Resonant separatrix layers
1.2.1 Layer dynamics
1.2.2 Approximate criteria
References
2 Hamiltonian Chaos in Pendulum
2.1 Resonance conditions
2.1.1 Conservative system
2.1.2 Resonance and energy increments
2.2 Stochastic layers
2.3 Resonant layers
2.3.1 Librational resonant layers
2.3.2 Rotational resonant layers
2.4 Numerical simulations
References
3 Parametric Chaos in Pendulum
3.1 Resonance and energy increment
3.1.1 Libration
3.1.2 Rotation
3.2 Parametric stochastic layers
3.2.1 Analytic predictions
3.2.2 Numerical predictions
3.2.3 Illustrations
3.2.4 Numerical simulations
3.3 Parametric resonant layers
3.3.1 Approximate predictions
3.3.2 Numerical illustrations
References
4 Nonlinear Discrete Systems
4.1 Definitions
4.2 Fixed points and stability
4.3 Stability switching theory
4.4 Bifurcation theory
References
5 Periodic Flows in Continuous Systems
5.1 Discretization-based methods
5.2 Discrete Fourier series
References
6 Periodic Motions to Chaos in Pendulum
6.1 Periodic motions in pendulum
6.1.1 Implicit discretization
6.1.2 Periodic motions
6.2 Bifurcation trees to chaos
6.2.1 Period-1 motions to chaos
6.2.2 Period-3 motions to chaos
6.2.3 Period-5 motions to chaos
6.3 Frequency-amplitude characteristics
6.3.1 Period-1 to period-4 motions
6.3.2 Period-3 to period-6 motions
6.3.3 Symmetric to asymmetric period-5 motions
6.4 Bifurcation trees varying with excitation amplitude
6.4.1 Non-travelable period-1 motions to chaos
6.4.2 Non-travelable period-3 motions to chaos
6.4.3 Travelable period-1 motions to chaos
6.4.4 Travelable period-2 motions to chaos
6.5 Numerical simulations
6.5.1 Non-travelable periodic motions
6.5.1.1 Period-1 to period-4 motions
6.5.1.2 Period-3 to period-6 motions
6.5.1.3 Period-5 motions
6.5.2 Travelable periodic motions
6.5.2.1 Travelable period-1 to period-2 motions
6.5.2.2 Travelable period-2 to period-8 motions
References
Subject Index
前辅文
1 Resonance and Hamiltonian Chaos
1.1 Stochastic layers
1.1.1 Definitions
1.1.2 Approximate criteria
1.2 Resonant separatrix layers
1.2.1 Layer dynamics
1.2.2 Approximate criteria
References
2 Hamiltonian Chaos in Pendulum
2.1 Resonance conditions
2.1.1 Conservative system
2.1.2 Resonance and energy increments
2.2 Stochastic layers
2.3 Resonant layers
2.3.1 Librational resonant layers
2.3.2 Rotational resonant layers
2.4 Numerical simulations
References
3 Parametric Chaos in Pendulum
3.1 Resonance and energy increment
3.1.1 Libration
3.1.2 Rotation
3.2 Parametric stochastic layers
3.2.1 Analytic predictions
3.2.2 Numerical predictions
3.2.3 Illustrations
3.2.4 Numerical simulations
3.3 Parametric resonant layers
3.3.1 Approximate predictions
3.3.2 Numerical illustrations
References
4 Nonlinear Discrete Systems
4.1 Definitions
4.2 Fixed points and stability
4.3 Stability switching theory
4.4 Bifurcation theory
References
5 Periodic Flows in Continuous Systems
5.1 Discretization-based methods
5.2 Discrete Fourier series
References
6 Periodic Motions to Chaos in Pendulum
6.1 Periodic motions in pendulum
6.1.1 Implicit discretization
6.1.2 Periodic motions
6.2 Bifurcation trees to chaos
6.2.1 Period-1 motions to chaos
6.2.2 Period-3 motions to chaos
6.2.3 Period-5 motions to chaos
6.3 Frequency-amplitude characteristics
6.3.1 Period-1 to period-4 motions
6.3.2 Period-3 to period-6 motions
6.3.3 Symmetric to asymmetric period-5 motions
6.4 Bifurcation trees varying with excitation amplitude
6.4.1 Non-travelable period-1 motions to chaos
6.4.2 Non-travelable period-3 motions to chaos
6.4.3 Travelable period-1 motions to chaos
6.4.4 Travelable period-2 motions to chaos
6.5 Numerical simulations
6.5.1 Non-travelable periodic motions
6.5.1.1 Period-1 to period-4 motions
6.5.1.2 Period-3 to period-6 motions
6.5.1.3 Period-5 motions
6.5.2 Travelable periodic motions
6.5.2.1 Travelable period-1 to period-2 motions
6.5.2.2 Travelable period-2 to period-8 motions
References
Subject Index
前辅文
1 Resonance and Hamiltonian Chaos
1.1 Stochastic layers
1.1.1 Definitions
1.1.2 Approximate criteria
1.2 Resonant separatrix layers
1.2.1 Layer dynamics
1.2.2 Approximate criteria
References
2 Hamiltonian Chaos in Pendulum
2.1 Resonance conditions
2.1.1 Conservative system
2.1.2 Resonance and energy increments
2.2 Stochastic layers
2.3 Resonant layers
2.3.1 Librational resonant layers
2.3.2 Rotational resonant layers
2.4 Numerical simulations
References
3 Parametric Chaos in Pendulum
3.1 Resonance and energy increment
3.1.1 Libration
3.1.2 Rotation
3.2 Parametric stochastic layers
3.2.1 Analytic predictions
3.2.2 Numerical predictions
3.2.3 Illustrations
3.2.4 Numerical simulations
3.3 Parametric resonant layers
3.3.1 Approximate predictions
3.3.2 Numerical illustrations
References
4 Nonlinear Discrete Systems
4.1 Definitions
4.2 Fixed points and stability
4.3 Stability switching theory
4.4 Bifurcation theory
References
5 Periodic Flows in Continuous Systems
5.1 Discretization-based methods
5.2 Discrete Fourier series
References
6 Periodic Motions to Chaos in Pendulum
6.1 Periodic motions in pendulum
6.1.1 Implicit discretization
6.1.2 Periodic motions
6.2 Bifurcation trees to chaos
6.2.1 Period-1 motions to chaos
6.2.2 Period-3 motions to chaos
6.2.3 Period-5 motions to chaos
6.3 Frequency-amplitude characteristics
6.3.1 Period-1 to period-4 motions
6.3.2 Period-3 to period-6 motions
6.3.3 Symmetric to asymmetric period-5 motions
6.4 Bifurcation trees varying with excitation amplitude
6.4.1 Non-travelable period-1 motions to chaos
6.4.2 Non-travelable period-3 motions to chaos
6.4.3 Travelable period-1 motions to chaos
6.4.4 Travelable period-2 motions to chaos
6.5 Numerical simulations
6.5.1 Non-travelable periodic motions
6.5.1.1 Period-1 to period-4 motions
6.5.1.2 Period-3 to period-6 motions
6.5.1.3 Period-5 motions
6.5.2 Travelable periodic motions
6.5.2.1 Travelable period-1 to period-2 motions
6.5.2.2 Travelable period-2 to period-8 motions
References
Subject Index
