Luo, Albert C. J. <br/><br/>
Analytical routes to chaos in nonlinear engineering / 
Albert C.J. Luo, Southern Illinois University, USA. 
 - x, 266 pages :  illustrations ;  25 cm. 
<br/><br/>Includes bibliographical references and index. 
<br/><br/>1. Introduction -- 2. Bifurcation Trees in Duffing Oscillators -- 3. Self-Excited Nonlinear Oscillators -- 4. Parametric Nonlinear Oscillators -- 5. Nonlinear Jeffcott Rotor Systems -- --  Introduction --  Analytical Methods --  Lagrange Standard Form --  Perturbation Methods --  Method of Averaging --  Generalized Harmonic Balance --  Book Layout --  Bifurcation Trees in Duffing Oscillators --  Analytical Solutions --  Period-1 Motions to Chaos --  Period-1 Motions --  Period-1 to Period-4 Motions --  Numerical Simulations --  Period-3 Motions to Chaos --  Independent, Symmetric Period-3 Motions --  Asymmetric Period-3 Motions --  Period-3 to Period-6 Motions --  Numerical Illustrations --  Self-Excited Nonlinear Oscillators --  van del Pol Oscillators --  Analytical Solutions --  Frequency-Amplitude Characteristics --  Numerical Illustrations --  van del Pol-Duffing Oscillators --  Finite Fourier Series Solutions --  Analytical Predictions --  Numerical Illustrations --  Parametric Nonlinear Oscillators --  Parametric, Quadratic Nonlinear Oscillators --  Analytical Solutions --  Analytical Routes to Chaos --  Numerical Simulations --  Parametric Duffing Oscillators --  Formulations --  Parametric Hardening Duffing Oscillators --  Nonlinear Jeffcott Rotor Systems --  Analytical Periodic Motions --  Frequency-Amplitude Characteristics --  Period-1 Motions --  Analytical Bifurcation Trees --  Independent Period-5 Motion --  Numerical Simulations.  1.  1.1.  1.1.1.  1.1.2.  1.1.3.  1.1.4.  1.2.  2.  2.1.  2.2.  2.2.1.  2.2.2.  2.2.3.  2.3.  2.3.1.  2.3.2.  2.3.3.  2.3.4.  3.  3.1.  3.1.1.  3.1.2.  3.1.3.  3.2.  3.2.1.  3.2.2.  3.2.3.  4.  4.1.  4.1.1.  4.1.2.  4.1.3.  4.2.  4.2.1.  4.2.2.  5.  5.1.  5.2.  5.2.1.  5.2.2.  5.2.3.  5.3. 
<br/><br/> "Nonlinear problems are of interest to engineers, physicists and mathematicians and many other scientists because most systems are inherently nonlinear in nature. As nonlinear equations are difficult to solve, nonlinear systems are commonly approximated by linear equations. This works well up to some accuracy and some range for the input values, but some interesting phenomena such as chaos and singularities are hidden by linearization and perturbation analysis. It follows that some aspects of the behavior of a nonlinear system appear commonly to be chaotic, unpredictable or counterintuitive. Although such a chaotic behavior may resemble a random behavior, it is absolutely deterministic. Analytical Routes to Chaos in Nonlinear Engineering discusses analytical solutions of periodic motions to chaos or quasi-periodic motions in nonlinear dynamical systems in engineering and considers engineering applications, design, and control. It systematically discusses complex nonlinear phenomena in engineering nonlinear systems, including the periodically forced Duffing oscillator, nonlinear self-excited systems, nonlinear parametric systems and nonlinear rotor systems. Nonlinear models used in engineering are also presented and a brief history of the topic is provided."--Publisher's website. 
<br/><br/><label>ISBN: </label>1118883942 9781118883945 
<br/><br/><label>LCCN: </label>2014001974 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Systems engineering<br/>Chaotic behavior in systems.<br/>Nonlinear systems.<br/>Nonlinear control theory.
<br/><br/><label>LC Class. No.: </label>TA168  / .L86 2014 
<br/><br/><label>Dewey Class. No.: </label>629.836