• Journal of Astronomy and Space Sciences
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• v.15 no.1
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• pp.209-220
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• 1998

The stability problem of steady motion of a rigid body with multi-elastic appendages and multi-liquid-filled cavities, in the presence of no external forces or torque, is considered in this paper. The flexible appendages are modeled as the clamped -free-free-free rectangular plates, or/and as the discrete mass- spring sub-system. The motion of liquid in every single ellipsoidal cavity is modeled as the uniform vortex motion with a finite number of degrees of freedom. Assuming that stationary holonomic constraints imposed on the body allow its rotation about a spatially fixed axis, the equation of motion for such a systematic configuration can be very complex. It consists of a set of ordinary differential equations for the motion of the rigid body, the uniform rotation of the contained liquids, the motion of discrete elastic parts, and a set of partial differential equations for the elastic appendages supplemented by appropriate initial and boundary conditions. In addition, for such a hybrid system, under suitable assumptions, their equations of motion have four types of first integrals, i.e., energy and area, Helmholtz' constancy of liquid - vortexes, and the constant of the Poisson equation of motion. Chetaev's effective method for constructing Liapunov functions in the form of a set of first integrals of the equations of the perturbed motion is employed to investigate the sufficient stability conditions of steady motions of the complete system in the sense of Liapunov, i.e., with respect to the variables determining the motion of the solid body and to some quantities which define integrally the motion of flexible appendages. These sufficient conditions take into account the vortexes of the contained liquids, the vibration of the flexible components, and coupling among the liquid-elasticity solid.

• Journal of Astronomy and Space Sciences
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• v.32 no.4
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• pp.335-340
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• 2015

Using the Total Electron Content (TEC) data from the Global Navigation Service System (GNSS) site in Jeju, operated by the Korea Astronomy and Space Science Institute (geographic location: $33.3^{\circ}N$, $126.5^{\circ}E$; geomagnetic location: $23.6^{\circ}N$) for 2002-2014 in Korea, the results of the statistical analysis of positive and negative ionospheric storms are presented for the first time. In this paper, ionospheric storms are defined as turbulences that exceed 50% of the percentage differential Global Positioning System (GPS) TEC ratio (${\Delta}TEC$) with monthly median GPS TEC. During the period of observations, the total number of positive ionospheric storms (${\Delta}TEC$ > 50%) was 170, which is greater than five times the number of negative ionospheric storms (${\Delta}TEC$ < - 50%) of 33. The numbers of ionospheric storms recorded during solar cycles 23 and 24 were 134 and 69, respectively. Both positive and negative ionospheric storms showed yearly variation with solar activity during solar cycle 23, but during solar cycle 24, the occurrence of negative ionospheric storms did not show any particular trend with solar activity. This result indicates that the ionosphere is actively perturbed during solar cycle 23, whereas it is relatively quiet during solar cycle 24. The monthly variations of the ionospheric storms were not very clear although there seems to be stronger occurrence during solstice than during equinox. We also investigated the variations of GPS positioning accuracy caused by ionospheric storms during November 7-10, 2004. During this storm period, the GPS positioning accuracies from a single frequency receiver are 3.26 m and 2.97 m on November 8 and 10, respectively, which is much worse than the quiet conditions on November 7 and 9 with the accuracy of 1.54 m and 1.69 m, respectively.