Nonlinear dynamics of the first order phase transition is investigated by using a kinetic mean-spherical model of spin-non-conserving type. A sum-rule condition for spin correlation functions brings in the nonlinear couplings between the long-range-order and fluctuations. The model serves as a simple approximation for the TDGL system. Unstable, far-from-equilibrium states are prepared by sudden changes of the external field and/or the temperature. The relaxation process starting with these states is composed of two stages, i.e., a rapid relaxation to the metastable state, which depends on the initial state and a slow relaxation to the true equilibrium state. The time scales of these two processes are well separated if the external field is sufficiently weak. During the process of relaxation there occurs a transient, anomalous increase of the fluctuation in the small wave-number range. This is the reason why the simple molecular field theory cannot be applied to these nonlinear problems.

Metastability

Hysteresis

Ginzburg–Landau theory

Mean field theory

10.1143/ptp.60.683

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Citations (5)

Simple Linearized Equation of Motion for Spinning Tops on a Table

Journal of System Design and Dynamics (2010)

Chikara Murakami

This paper deals with deriving a simple linearized equation of motion for axisymmetric tops spinning on a table; the equation includes the effects of both friction and gravitation. The derived equation is a single second-order equation with complex number coefficients. The main variable is the inclination angle of the spinning axis, which is expressed by a single complex number. No Euler's angle is used. The precondition for linearization is that both the angular momentum vector and the spinning axis are close to the zenith direction. The friction is assumed to be viscous, and the friction torque can be expressed by using the height of the gravity center and the radius of the curvature at the contact point to the table. Two eigenvalues for the equation give a deep insight into the attitude behavior. The root-locus method was applied to explain the spinning motion stability of various axisymmetric bodies. An analytical solution for a horizontally suspended spinning top is given to show that the locus of the spinning axis is a trochoid.

Circular motion

10.1299/jsdd.4.142

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Citations (2)

On orbit control using gravity gradient effects

Acta Astronautica (1981)

Chikara Murakami

Orbit (dynamics)

10.1016/0094-5765(81)90014-x

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Citations (17)

A compact magnetic bearing for gimballed momentum wheel

Kazuyoshi Yabuuchi M. Inoue Sadao Akishita Chikara Murakami Osamu Okamoto

A three axis controlled magnetic bearing and its application to a momentum wheel are described. The four divided stators provide a momentum wheel with high reliability, low weight, large angular momentum storage capacity, and gimbal control. Those characteristics are desirable for spacecraft attitude control.

Magnetic bearing

Reaction wheel

Momentum (technical analysis)

Control moment gyroscope

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Citations (4)

A Design Method of Dynamic Compensator for Magnetic Bearings of a Rigid Spinning Rotor.

IEEJ Transactions on Industry Applications (1991)

Chikara Murakami

A design method of a dynamic compensator for magnetic bearings levitating a spinning rigid rotor is proposed. The control strategy is to move the angular momentum vector to the spinning axis for nutation (short period mode) suppression and to move the vector to the central position of the stator for precession (long period mode) suppression. It is necessary to estimate the angular momentum vector. A simple estimation method is proposed here without using observer system or rate signals of attitude angles. Low pass filters are used to obtain low frequency compoments, which nearly equal the angular momentum vector, from the observed attitude signals. It is shown that phase lag effects of the filter can be compensated by cross-feedback, whose physical meaning is clarified by a block diagram of the total system including the dynamic compensator. Stability is discussed using root locus method. Several numerical simulation examples are given, showing effectiveness of the method.

Root locus

Control moment gyroscope

Observer (physics)

Nutation

Magnetic bearing

10.1541/ieejias.111.1097

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Citations (1)

509 Extending Applicable Area for a Linearized Equation of Spinning Tops.

The Proceedings of the Dynamics & Design Conference (2005)

Chikara Murakami

This paper deals with extension of applicable area for the linearized equation of motion of spinning tops on the table which has been derived more than ten years ago by the auther. At first, the linearized equation which is only second order with complex number coefficients is again introduced. Friction torque is supposed to be viscous type and the coefficients can be expressed using heights of gravity center and radius of curveture at contact point. Applicability of the equation is limitted to the narrow region. In this paper, if, angular momentum vectors are sufficiently large and close to the zenith direction, it is shown that the attitude behavior can be described using the azimuthal equidistant projection. Two examples which are horizontally-suspended tops and the boiled eggs inclined more than about 45[deg] are shown.

TOPS

Equidistant

10.1299/jsmedmc.2005._509-1_

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206 Fundamental Experiments of Simplified Magnetic Seesaw Damper

The Proceedings of the Symposium on the Motion and Vibration Control (2001)

Chikara Murakami Kohei SUZUKI

The original magnetic seesaw danper has two magnetic paths which branch off from magnetic pole pieces via gaps. In other words, between two yokess, exists a permanent magnet having two pole pieces. Each side has two gaps which increase or decrease oppositely to the other side gaps, i.e., all four gaps change their length due to extermal vibration. Therefore, its rather tedious to adjust strength of mechanical spring constants to overcome unstable force. In this paper, it is proposed that any one side gaps is fixes to a constance, introducing simple structure and easy adjustment. However, some decrease of damping are unavoidable. Some experimental data are given.

10.1299/jsmemovic.2001.7.198

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A Thermokinetic Model for Excitation Phenomena

Seibutsu Butsuri (1979)

Chikara Murakami Kazuhisa Tomita

Giant transitory excitation, as is familiar in nerve impulse propagation, is derived from a simple thermokinetic model. Excitations of all-or-none type, the graded type, and also the repetitive pulsing have been derived from a single model depending on the value of control parameter. The temperature, or the concentration of enetgy is included as an independent reference variable which is affected by the reaction heat. The rate of reaction is affected in turn by the temperature through Arrhenius' formula. The strong nonlinearity involved in the Arrhenius' formula leads to a multiple steady state which is connected with the existence of a threshold for the excitation. The dynamic large excursion along an almost closed path in phase space is related to the existence of a nearby limit cycle, which is generated by an inverted bifurcation. Thus the interplay of the soft-and hard-mode instabilities is shown to form the background of the giant transitory excitation.The transition into repetitive pulsing is also investigated from the point of view of fluctuation which reflects the difference between normal and inverted bifurcation.

Limit cycle

10.2142/biophys.19.229

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Magnetically suspended flywheel for satellite

Chikara Murakami Yoshiaki Ohkami Shimamoto Akitoshi Takahashi S. Shingu

Flywheel

Source

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