Browsing by Author "Ku, FN"

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A Melnikov method for strongly odd nonlinear oscillators
(1998-03-01)
Ge, ZM
;
Ku, FN
;
機械工程學系
;
Department of Mechanical Engineering
In this paper. explicit calculations that extend the applicability of the Melnikov method to include strongly odd nonlinear and large forcing amplitude oscillating systems, are presented. We consider the response of the strongly nonlinear oscillating system governed by an equation of motion containing a parameter epsilon which need not be small. Phenomena considered are steady state response of strongly nonlinear oscillators subject to harmonic excitation. Two examples are given, they are the strongly nonlinear Duffing's equation and a pendulum suspended on a rotating arm. Finally, a adjustable factor is used to fit the simulation data. The theoretical chaotic behavior regions thus defined and plotted in the forcing amplitude versus parameter plane give the lower bounds for the true chaotic motion zones.
Dynamic analysis of a gyrocompass
(1996-09-01)
Ge, ZM
;
Lue, YC
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Ku, FN
;
機械工程學系
;
Department of Mechanical Engineering
After giving the mathematical relation of the offset angle connection between the inner ring and the ballistic, and the mathematical model of the follow-up subsystem, the exact governing equations of gyrocompass with ballistic are given by Lagrange's equations. The explanation of the asymptotical stability about the system equilibrium by Arnold (1961) is shown to be wrong. Then use Liapunov theorem and Mukherjee-Chen theorem (1993) of direct method, Routh-Hurwitz criterion and multiple scales method are applied to study the stability about the equilibrium of the system in some cases.
Dynamic analysis of a gyrocompass
(1996-09-01)
Ge, ZM
;
Lue, YC
;
Ku, FN
;
交大名義發表
;
機械工程學系
After giving the mathematical relation of the offset angle connection between the inner ring and the ballistic, and the mathematical model of the follow-up subsystem, the exact governing equations of gyrocompass with ballistic are given by Lagrange's equations. The explanation of the asymptotical stability about the system equilibrium by Arnold (1961) is shown to be wrong. Then use Liapunov theorem and Mukherjee-Chen theorem (1993) of direct method, Routh-Hurwitz criterion and multiple scales method are applied to study the stability about the equilibrium of the system in some cases.
Dynamic analysis of a two-gyro Anschutz compass
(1997-01-01)
Ge, ZM
;
Jen, CW
;
Ku, FN
;
機械工程學系
;
Department of Mechanical Engineering
In this paper, the dynamics of the two-gyro Anschutz compass in two cases, i.e. the earth spin velocity and zero vehicle velocity case, as well as the earth spin velocity and non-zero vehicle case, are studied. The detailed exact equations of motion of this compass are obtained by Lagrange's equations. The system is studied by the linear approximation method, and these equations are solved as eigenvalue problems. The stabilities of these motions are also discussed. The analytical stabilities for two cases from the linear approximation method are checked by the numerical solutions.
Dynamic analysis of a two-gyro Anschutz compass
(1997-01-01)
Ge, ZM
;
Jen, CW
;
Ku, FN
;
交大名義發表
;
機械工程學系
In this paper, the dynamics of the two-gyro Anschutz compass in two cases, i.e. the earth spin velocity and zero vehicle velocity case, as well as the earth spin velocity and non-zero vehicle case, are studied. The detailed exact equations of motion of this compass are obtained by Lagrange's equations. The system is studied by the linear approximation method, and these equations are solved as eigenvalue problems. The stabilities of these motions are also discussed. The analytical stabilities for two cases from the linear approximation method are checked by the numerical solutions.
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.
Stability of Euler, Lagrange and Kovalevskaya gyros in a Newtonian central force field with second order terms
(1996)
Ge, ZM
;
Ku, FN
;
交大名義發表
;
機械工程學系
;
National Chiao Tung University
The stability of the permanent rotation of the Euler, Lagrange and Kovalevskaya gyros about a fixed point in the Newtonian central force field is investigated by Liapunov direct method, which improve Leimanis' and Rumiantsev's result of stability conditions. For the sake of high accuracy, the first and second order terms of R(-1) expressed by potential energy of the Newtonian central force field have been considered, where the R is the distance from the fixed point to the center of attraction.
Stability of Euler, Lagrange and Kovalevskaya gyros in a Newtonian central force field with second order terms (vol 20, pg 53, 1996)
(1996)
Ge, ZM
;
Ku, FN
;
交大名義發表
;
機械工程學系
;
National Chiao Tung University
Stability, bifurcation and chaos of a pendulum on a rotating arm
(1997-11-01)
Ge, ZM
;
Ku, FN
;
機械工程學系
;
Department of Mechanical Engineering
This paper presents an analytical and numerical study of the dynamical behavior of a pendulum on a rotating arm. There are four control parameters, which influences the behaviors of mechanical system, namely: the length ratio of the arm to pendulum, the damping, the frequency and the gravity force. The sufficient conditions for the stability are obtained using damped Mathieu equation theory and the Lyapunov direct method. It is found that stable equilibrium positions depend on four control parameters, the gravity force that appears as as an oscillating exciting torque and the length ratio in system causes the existence of a chaotic attractor or regular, several different types of transitions to chaos are studied. The Melnikov method is used to show the existence of chaotic motion. The treatment of the Melnikov integral is different for different length ratio. The magnitude effects of the length ratio parameter is important to acknowledge the existence of a chaotic attractor or regular motion. Moreover, numerical simulations including bifurcation diagrams are constructed to investigate dynamical behavior of the system. The transitions to chaos are confirmed by calculation of Lyapunov exponents. More detailed numerical investigations appear in phase trajectories and Poincare maps.
Stability, bifurcation and chaos of a pendulum on a rotating arm
(1997-11-01)
Ge, ZM
;
Ku, FN
;
機械工程學系
;
Department of Mechanical Engineering
This paper presents an analytical and numerical study of the dynamical behavior of a pendulum on a rotating arm. There are four control parameters, which influences the behaviors of mechanical system, namely: the length ratio of the arm to pendulum, the damping, the frequency and the gravity force. The sufficient conditions for the stability are obtained using damped Mathieu equation theory and the Lyapunov direct method. It is found that stable equilibrium positions depend on four control parameters, the gravity force that appears as as an oscillating exciting torque and the length ratio in system causes the existence of a chaotic attractor or regular, several different types of transitions to chaos are studied. The Melnikov method is used to show the existence of chaotic motion. The treatment of the Melnikov integral is different for different length ratio. The magnitude effects of the length ratio parameter is important to acknowledge the existence of a chaotic attractor or regular motion. Moreover, numerical simulations including bifurcation diagrams are constructed to investigate dynamical behavior of the system. The transitions to chaos are confirmed by calculation of Lyapunov exponents. More detailed numerical investigations appear in phase trajectories and Poincare maps.
Subharmonic Melnikov functions for strongly odd non-linear oscillators with large perturbations
(2000-09-21)
Ge, ZM
;
Ku, FN
;
機械工程學系
;
Department of Mechanical Engineering