Geography of Order and Chaos in Mechanics
Cordani, Bruno.
Geography of Order and Chaos in Mechanics Investigations of Quasi-Integrable Systems with Analytical, Numerical, and Graphical Tools / [electronic resource] : by Bruno Cordani. - XVIII, 334 p. online resource. - Progress in Mathematical Physics ; 64 . - Progress in Mathematical Physics ; 64 .
Preface -- List of Figures -- 1 Introductory Survey -- 2 Analytical Mechanics and Integrable Systems -- 3 Perturbation Theory -- 4 Numerical Tools I: ODE Integration -- 5 Numerical Tools II: Detecting Order, Chaos, and Resonances -- 6 The Kepler Problem -- 7 The KEPLER Program -- 8 Some Perturbed Keplerian Systems -- 9 The Multi-Body Gravitational Problem -- Bibliography -- Index.
This original monograph aims to explore the dynamics in the particular but very important and significant case of quasi-integrable Hamiltonian systems, or integrable systems slightly perturbed by other forces. With both analytic and numerical methods, the book studies several of these systems—including for example the hydrogen atom or the solar system, with the associated Arnold web—through modern tools such as the frequency-modified fourier transform, wavelets, and the frequency-modulation indicator. Meanwhile, it draws heavily on the more standard KAM and Nekhoroshev theorems. Geography of Order and Chaos in Mechanics contains many figures that illuminate its concepts in novel ways, but perhaps its most useful feature is its inclusion of software to reproduce the various numerical experiments. The graphical user interfaces of five supplied MATLAB programs allows readers without any knowledge of computer programming to visualize and experiment with the distribution of order, chaos and resonances in various Hamiltonian systems. This monograph will be a valuable resource for professional researchers and certain advanced undergraduate students in mathematics and physics, but mostly will be an exceptional reference for Ph.D. students with an interest in perturbation theory.
9780817683702
10.1007/978-0-8176-8370-2 doi
Mathematics.
Partial differential equations.
Differential geometry.
Mathematical physics.
Physics.
Statistical physics.
Mathematics.
Mathematical Physics.
Differential Geometry.
Nonlinear Dynamics.
Partial Differential Equations.
Numerical and Computational Physics.
Mathematical Methods in Physics.
QA401-425 QC19.2-20.85
530.15
Geography of Order and Chaos in Mechanics Investigations of Quasi-Integrable Systems with Analytical, Numerical, and Graphical Tools / [electronic resource] : by Bruno Cordani. - XVIII, 334 p. online resource. - Progress in Mathematical Physics ; 64 . - Progress in Mathematical Physics ; 64 .
Preface -- List of Figures -- 1 Introductory Survey -- 2 Analytical Mechanics and Integrable Systems -- 3 Perturbation Theory -- 4 Numerical Tools I: ODE Integration -- 5 Numerical Tools II: Detecting Order, Chaos, and Resonances -- 6 The Kepler Problem -- 7 The KEPLER Program -- 8 Some Perturbed Keplerian Systems -- 9 The Multi-Body Gravitational Problem -- Bibliography -- Index.
This original monograph aims to explore the dynamics in the particular but very important and significant case of quasi-integrable Hamiltonian systems, or integrable systems slightly perturbed by other forces. With both analytic and numerical methods, the book studies several of these systems—including for example the hydrogen atom or the solar system, with the associated Arnold web—through modern tools such as the frequency-modified fourier transform, wavelets, and the frequency-modulation indicator. Meanwhile, it draws heavily on the more standard KAM and Nekhoroshev theorems. Geography of Order and Chaos in Mechanics contains many figures that illuminate its concepts in novel ways, but perhaps its most useful feature is its inclusion of software to reproduce the various numerical experiments. The graphical user interfaces of five supplied MATLAB programs allows readers without any knowledge of computer programming to visualize and experiment with the distribution of order, chaos and resonances in various Hamiltonian systems. This monograph will be a valuable resource for professional researchers and certain advanced undergraduate students in mathematics and physics, but mostly will be an exceptional reference for Ph.D. students with an interest in perturbation theory.
9780817683702
10.1007/978-0-8176-8370-2 doi
Mathematics.
Partial differential equations.
Differential geometry.
Mathematical physics.
Physics.
Statistical physics.
Mathematics.
Mathematical Physics.
Differential Geometry.
Nonlinear Dynamics.
Partial Differential Equations.
Numerical and Computational Physics.
Mathematical Methods in Physics.
QA401-425 QC19.2-20.85
530.15