Browsing by Author "Chen, HK"

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Anti-control of chaos in rigid body motion
(2004-08-01)
Chen, HK
;
Lee, CI
;
機械工程學系
;
Department of Mechanical Engineering
Anti-control of chaos for a rigid body has been studied in the paper. For certain feedback gains, a rigid body can easily generate chaotic motion. Basic dynamical behaviors, such as symmetry, invariance, dissipativity and existence of attractor, are also discussed. The transient behaviors of the chaotic system have also been presented as the feedback gain changed. Of particular interesting is the fact that the chaotic system can generate a complex multi-scroll chaotic attractor under the appropriate feedback gains. Finally, it was shown that the system could be related to the famous Lorenz equations and Chen system. In other words, the system can easily display all the dynamical behaviors of the famous Lorenz equations and Chen system. (C) 2003 Elsevier Ltd. All rights reserved.
Bifurcations and chaos of a two-degree-of-freedom dissipative gyroscope
(2005-04-01)
Chen, HK
;
Ge, ZM
;
機械工程學系
;
Department of Mechanical Engineering
The dynamic behaviors of a dissipative gyroscope mounted on a vibrating base are investigated qualitatively and numerically. It is shown that the nonlinear system can exhibit regular and chaotic motions. The qualitative behaviors of the system are studied by the center manifold theorem and the normal form theorem. The co-dimension one bifurcation analysis for the Hopf bifurcation is carried out. The pitchfork, Hopf, and saddle connection bifurcations for co-dimension two bifurcation are also found in this study. Regular and chaotic motions are shown to be possible in the parameter space. Numerical methods are used to obtain the time histories, the Poincare maps, the Liapunov exponents, and the Liapunov dimensions. The effect of the spin speed of the gyroscope on its dynamic behavior is also studied by numerical simulation in conjunction with the Liapunov exponents, and it has been found that the higher spin speed of the gyroscope can quench the chaotic motion. (C) 2004 Elsevier Ltd. All rights reserved.
Global stability of a shielded dual-spin satellite
(1996)
Ge, ZM
;
Chen, HK
;
交大名義發表
;
機械工程學系
;
National Chiao Tung University
Sufficient conditions for the global stabilities of equilibrium positions of a dual-spin satellite equipped with a cylindrical electrostatic screen normal to the circular equatorial orbital plane system under the action of moments induced by the gravitational and Lorentz forces are obtained by Liapunov's direct method. The problem is then studied with respect to all variables, including the angular velocity of the rotor. The instabilities of the problem are solved by the first approximation theorem. Furthermore, sufficient conditions for the global stability of rotation with arbitrary angular velocity for an axisymmetric dual-spin satellite equipped with an electrostatic screen me presented by applying Liapunov's direct method.
Improved stability of a dual-spin satellite in circular orbit
(1997-02-01)
Ge, ZM
;
Chen, HK
;
交大名義發表
;
機械工程學系
;
National Chiao Tung University
Sufficient conditions for the global stability of equilibrium positions of a dual-spin satellite in a circular orbital system in a Newtonian central force field are obtained by Liapunov's direct method. The new results are compared with those already known. The problem is then studied with respect to all variables, including the angular velocity of the rotor. Further, sufficient conditions for the global stability of rotation with arbitrary angular velocity for an axisymmetric dual-spin satellite are presented by Liapunov's direct method, which improve on Kane's result of infinitesimal stability obtained by linearized equations of motion.
Low-frequency noise characteristics of hot carrier-stressed buried-channel pMOSFETs
(1998-03-01)
Jang, SL
;
Chen, HK
;
Chang, KM
;
電子工程學系及電子研究所
;
Department of Electronics Engineering and Institute of Electronics
Prestress and poststress low-frequency noise characteristics of buried-channel LDD pMOS-FETs have been studied. The devices were stressed at low gate and high drain bias, and the poststress drain current increases due to the hot-electron induced channel shortening effect. The noise measurements were carried out between 10 Hz and 100 kHz, 1/f(1.2) and generation-recombination current noises have been found in the drain current noises. The poststress 1/f(1.2) drain current noise increases in both the linear and saturation regime. This behavior is attributed to the increase of interface states and oxide electron charges after stress. (C) 1998 Elsevier Science Ltd. All rights reserved.
Regular and chaotic dynamics of a rotational machine with a centrifugal governor
(1999-05-01)
Ge, ZM
;
Yang, HS
;
Chen, HH
;
Chen, HK
;
機械工程學系
The dynamic behavior of a rotational machine with centrifugal governor which is subjected to two different forms of external disturbance is studied in this paper. The Lyapunov direct method is applied to obtain conditions of stability of the equilibrium points of the system. A codimension one bifurcation analysis for the autonomous system is carried out near the degenerate point. It is found that a Hopf bifurcation occurs in the system. The incremental harmonic balance (IHB) method combined with the multi-variable Floquet theory has been effectively applied to obtain the steady state responses of the three-dimensional nonautonomous system. Phase portraits, power spectra, Poincare maps, and Lyapunov exponents are presented to observe periodic, quasi-periodic and chaotic motions. (C) 1999 Elsevier Science Ltd. All rights reserved.
Stability and chaotic motions of a symmetric heavy gyroscope
(1996-03-01)
Ge, ZM
;
Chen, HK
;
交大名義發表
;
機械工程學系
;
National Chiao Tung University
The nonlinear motion of a symmetric heavy gyro mounted on a vibrating base, particularly its long-term dynamic behavior for a wide range of parameters, is investigated, The system exhibits both regular and chaotic motions. Two typical routes to chaos, namely through period-doubling and intermittency, are found in this study, The method of multiple scales is used to analyze the responses and to determine the stability of the trivial fixed point for the system excited by single harmonic force. The stability of the system excited by multiple harmonic forces has been studied by Lyapunov's direct method. As the system is subjected to external disturbance, the Melnikov method is used to show the existence of chaotic motion. The effect of the number of forcing frequencies on the chaotic regions is also established. The numerical results, in which the existence of chaos is demonstrated, are presented in the form of bifurcation diagrams, phase portraits, Poincare maps, and Lyapunov exponents. The effect of the gyroscope's spinning speed is also studied. It is found that increasing the gyroscope's spin speed is the simplest method to overcome the chaotic motion for this system.
Stability and instability of an Earth satellite with a cylindrical shield in the Newtonian central force field for accuracy
(1997-09-01)
Ge, ZM
;
Ku, FN
;
Chen, HK
;
機械工程學系
;
Department of Mechanical Engineering
The stability and instability of motion of an artificial Earth satellite equipped with a cylindrical electrostatic shield in a circular equatorial orbit is studied, The satellite traveling through the Earth's magnetic field causes Lorentz forces. For the sake of accuracy, the second-order terms of R-1 are retained for the potential function of the Newtonian central force field, The Lorentz forces and Newtonian central force field have an effect on the stability and instability affect the conditions. Right equilibrium positions of the satellite in the orbital coordinate system are considered, Furthermore, we study the stability of motion when the axisymmetric shielded satellite rotates at an arbitrary speeds in a circular orbit under the influence of gravitational forces and Lorentz forces. Finally, as the numerical examples show, the stable results present periodic oscillation about the zero solutions, The Lorentz forces lead to low frequency in the system, the third mass moment in the Newtonian central force field becomes more accurate, and the cumulative effect is considerable.
The regular and chaotic motions of a symmetric heavy gyroscope with harmonic excitation
(1996-11-28)
Ge, ZM
;
Chen, HK
;
Chen, HH
;
機械工程學系
;
Department of Mechanical Engineering
The non-linear motion of a symmetric gyro mounted on a vibrating base is investigated, with particular emphasis on its long-term dynamic behaviour for a wide range of parameters. A single modal equation is used to analyze the qualitative behavior of the system. External disturbance appears as vertical harmonic motion of the support point and linear damping is assumed. The complete equation of motion is a non-linear non-autonomous one. The stability of the system has been studied by damped Mathieu equation theory and the Liapunov direct method. As the system is subjected to external disturbance, the Melnikov method is used to show the existence of chaotic motion. Finally, the bifurcation of the parameter dependent system is studied numerically. The time evolutions of the non-linear dynamical system responses are described in phase portraits via the Poincare map technique. The occurrence and the nature of chaotic attractors are verified by evaluating Liapunov exponents and average power spectra. The effect of the gyroscope's spinning speed is also studied, and it is shown that the gyroscope's spin velocity oz has a significant effect on the dynamic behavior of the motion. (C) 1996 Academic Press Limited
The regular and chaotic motions of a symmetric heavy gyroscope with harmonic excitation
(1996-11-28)
Ge, ZM
;
Chen, HK
;
Chen, HH
;
交大名義發表
;
機械工程學系
The non-linear motion of a symmetric gyro mounted on a vibrating base is investigated, with particular emphasis on its long-term dynamic behaviour for a wide range of parameters. A single modal equation is used to analyze the qualitative behavior of the system. External disturbance appears as vertical harmonic motion of the support point and linear damping is assumed. The complete equation of motion is a non-linear non-autonomous one. The stability of the system has been studied by damped Mathieu equation theory and the Liapunov direct method. As the system is subjected to external disturbance, the Melnikov method is used to show the existence of chaotic motion. Finally, the bifurcation of the parameter dependent system is studied numerically. The time evolutions of the non-linear dynamical system responses are described in phase portraits via the Poincare map technique. The occurrence and the nature of chaotic attractors are verified by evaluating Liapunov exponents and average power spectra. The effect of the gyroscope's spinning speed is also studied, and it is shown that the gyroscope's spin velocity oz has a significant effect on the dynamic behavior of the motion. (C) 1996 Academic Press Limited
The stability of the rotation of a magnetized gyro with a fixed point
(1996-03-01)
Ge, ZM
;
Chen, HK
;
交大名義發表
;
機械工程學系
;
National Chiao Tung University
In conventional studies about the gyro motion the gyroscopic forces which are produced by the Lorentz action of the magnetic field on the electrical charges moving in space have not been considered. Euler gyro, Lagrange gyro and Kovalveskaya gyro are three representative gyros. In this paper, the stability and instability conditions of the rotation of the three representative gyros under the action of the Lorentz forces both in a uniform force field and in a central force field are obtained by using Liapunov's direct method.
Three asymptotical stability theorems on partial region with applications
(1998-05-01)
Ge, ZM
;
Yu, JK
;
Chen, HK
;
機械工程學系
;
Department of Mechanical Engineering
For a long time, all stability theorems are concerned with the stability of the zero solution of the differential equations of disturbed motion on the whole region of the neighborhood of the origin. But for various problems of dynamical systems, the stability is actually on partial region. In other words, the traditional mathematical model is unmatched with the dynamical reality and artificially sets too strict demand which is unnecessary. In order to fill the gap between the traditional mathematical model and dynamical reality of various systems, three asymptotical stability theorems on partial region are given and nine applications are presented.