Download PDF by Yanzhu Liu: Chaos in Attitude Dynamics of Spacecraft

By Yanzhu Liu

ISBN-10: 3642300790

ISBN-13: 9783642300790

ISBN-10: 3642300804

ISBN-13: 9783642300806

Attitude dynamics is the theoretical foundation of angle regulate of spacecrafts in aerospace engineering. With the improvement of nonlinear dynamics, chaos in spacecraft perspective dynamics has drawn nice realization because the 1990's. the matter of the predictability and controllability of the chaotic angle movement of a spacecraft has a realistic importance in astronautic technological know-how. This ebook goals to summarize simple strategies, major methods, and up to date growth during this region. It makes a speciality of the study paintings of the writer and different chinese language scientists during this box, delivering new equipment and viewpoints within the research of spacecraft angle movement, in addition to new mathematical versions, with convinced engineering backgrounds, for extra analysis.

Professor Yanzhu Liu was once the Director of the Institute of Engineering Mechanics, Shanghai Jiao Tong college, China. Dr. Liqun Chen is a Professor on the division of Mechanics, Shanghai college, China.

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The average of many resulting { p j } will approximate the discrete power spectrum defined by Eq. 10). 9). That is the basic idea of the fast Fourier transform attributed to Cooley and Tukey [15]. Nowadays, there are many commercial software packages available for determining the fast Fourier transform of a given signal. The spectrum of a periodic motion with period T consists of discrete spikes at the frequency 1/T and possibly a certain number of other spikes at m/T for an integer m. The spectrum of a k-period quasiperiodic motion is made up of spikes at 43 Chaos in Attitude Dynamics of Spacecraft integer multiples of all its frequencies.

The Melnikov function is an explicitly computable function that can be evaluated analytically or numerically. The Melnikov theory has been extended to multi-degree-of-freedom systems [18] and infinite-degree-of-freedom systems [19, 20]. A generalized version for Hamiltonian systems with finite degrees-of-freedom will be presented in the next section, and it will be applied in the subsequent chapters. 50 Chapter 2 A Survey of Chaos Theory It should be kept in mind that the Melnikov theory only predicts transverse intersections of stable and unstable manifolds, or the existence of a homoclinic point.

The vector x is called a state vector, and Rn in which x evolves is called a state space. A stage space is called a phase space when half of the state variables are displacements and the other half are velocities. Obviously, the phase space is the generalization of the phase plane. If the vector function does not depend explicitly on time t, the dynamical system governed by Eq. 1) is call autonomous; otherwise, it is called nonautonomous. The geometrical structure representing an asymptotically long-time behavior in a state space is called an attractor.

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Chaos in Attitude Dynamics of Spacecraft by Yanzhu Liu


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