Accounting for non-stationary effects in the model of the Earth’s pole motion

2020 ◽  
Author(s):  
Yan Wai
Keyword(s):  
Average Frequency ◽  
Dissipative Systems ◽  
Main Process ◽  
Frequency Model ◽  
Steady State Condition ◽  
Pole Motion ◽  
The Earth ◽  
Earth Pole ◽  
Constant Coefficients ◽  
Linear Differential

<p><strong>Accounting for non-stationary effects in the model of the Earth’s pole motion</strong></p><p>Wai Yan Soe, Rumyantsev D.S., Perepelkin V.V.</p><p> </p><p>Nowadays the problem of constructing a model of the Earth pole motion is relevant both in theoretical and in applied aspects. The main difficulty of accurately describing the Earth pole motion is that it has non-stationary perturbations leading to the changes in both the average parameters of its motion and the motion as a whole.</p><p>The main process of the Earth pole coordinates fluctuations is the sum of the quasi periodic Chandler component and annual one. The approximation of the Earth pole motion is generally accepted to be a few parametric two-frequency model with constant coefficients. Relatively slow changes in the parameters of the Chandler and annual components make it possible to use this approximation in the time intervals of 6–7 years, that is, during the period of the Chandler and annual components modulation. This model has low algorithmic complexity and describes the main process of pole oscillations with acceptable accuracy.</p><p>However, due to the non-stationary perturbations there are effects in the Chandler and annual components that are not typical for a simple dynamical system that is described by linear differential equations with constant coefficients. Such changes can also be observed in the dissipative systems with not only with the amplitude variations but also when oscillation process is in steady-state condition [1].</p><p>In this work the effect of changing in the Earth pole oscillatory mode is revealed, which consists in a jump-like shift in the average frequency of the pole around the midpoint (the motion of the Earth pole midpoint is a pole trend of a long-period and secular nature), which leads to a change in the average speed of its motion.</p><p>A method is proposed to determine the moment when the average frequency is shifted, which is important for refining the forecast model of the Earth pole motion. Using this method a modified model of pole motion is developed and the dynamic effects in its motion are considered, caused by the change in the amplitudes ratio of the Chandler and annual harmonics.</p><p><strong>References</strong></p><p>[1] Barkin M.Yu., Krylov S.S., Perepelkin V.V. Modeling and analysis of the Earth pole motion with nonstationary perturbations. IOP Conf. Series: Journal of Physics: Conf. Series 1301 (2019) 012005; doi:10.1088/1742-6596/1301/1/012005</p><p> </p>

Modeling the Earth-pole motion for a short period of time

2009 ◽  
Vol 54 (5) ◽  
pp. 233-237
Author(s):  
L. D. Akulenko ◽  
Yu. G. Markov ◽  
V. V. Perepelkin
Keyword(s):  
Pole Motion ◽  
The Earth ◽  
Short Period ◽  
Earth Pole

Comparisons of Simulation Methods for Motions of a Moored Body in Waves

1985 ◽  
Vol 107 (1) ◽  
pp. 34-41
Author(s):  
M. Takagi ◽  
K. Saito ◽  
S. Nakamura
Keyword(s):  
Wave Theory ◽  
Simulation Methods ◽  
Convolution Integral ◽  
Linear Water Wave Theory ◽  
Initial Stage ◽  
Constant Coefficients ◽  
Exciting Forces ◽  
Linear Differential ◽  
Experimental Values ◽  
The Time Domain

Based on the linear water wave theory, numerical simulations are carried out for motions in waves of a body moored by a nonlinear-type mooring system. Numerical results obtained by using the equation of motion described in the time domain with a convolution integral (C.I. method) are compared with those of the second-order linear differential equation with constant coefficients (C. C. method). These results are also compared with experimental values measured from the initial stage when the action of exciting forces starts and the validity of C.I. method is discussed.

scholarly journals A graphical solution of a differential equation with application to hill’s treatment of nerve excitation

1937 ◽  
Vol 123 (832) ◽  
pp. 382-395 ◽  
Keyword(s):  
Viscous Medium ◽  
Graphical Solution ◽  
Initial Value ◽  
First Order ◽  
Rate Dependent ◽  
Monomolecular Reaction ◽  
Constant Coefficients ◽  
Linear Differential ◽  
Physical And Chemical ◽  
Nerve Excitation

Linear differential equations with constant coefficients are very common in physical and chemical science, and of these, the simplest and most frequently met is the first-order equation a dy / dt + y = f(t) , (1) where a is a constant, and f(t) a single-valued function of t . The equation signifies that the quantity y is removed at a rate proportional to the amount present at each instant, and is simultaneously restored at a rate dependent only upon the instant in question. Familiar examples of this equation are the charging of a condenser, the course of a monomolecular reaction, the movement of a light body in a viscous medium, etc. The solution of this equation is easily shown to be y = e - t / a { y 0 = 1 / a ∫ t 0 e t /a f(t) dt , (2) where y 0 is the initial value of y . In the case where f(t) = 0, this reduces to the well-known exponential decay of y .

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