Numerical Simulation of the Rotational Motion of the Earth and Moon

1997 ◽  
Vol 165 ◽  
pp. 275-280
Author(s):  
G.I. Eroshkin ◽  
V.V. Pashkevich
Keyword(s):  
Numerical Simulation ◽  
Analytical Solutions ◽  
Rotational Motion ◽  
Analytical Theory ◽  
Time Interval ◽  
Mean Square ◽  
Physical Libration ◽  
Motion Equations ◽  
The Earth ◽  
Systematic Character

AbstractDynamics of the rotational motion of the Earth and Moon is investigated numerically. Very convenient Rodrigues-Hamilton parameters are used for high-precision numerical integration of the rotational motion equations in the post-newtonian approximation over a 400 yr time interval. The results of the numerical solution of the problem are compared with the contemporary analytical theories of the Earth’s and Moon’s rotation. The analytical theory of the Earth’s rotation is composed of the precession theory (Lieske et al., 1977), nutation theory (Souchay and Kinoshita, 1996) and geodesic nutation solution (Fukushima, 1991). The analytical theory of the Moon’s rotation consists of the so-called Cassini relations and the analytical solutions of the lunar physical libration problem (Moons, 1982), (Moons, 1984), (Pešek, 1982). The comparisons reveal residuals both of periodic and systematic character. All the secular and periodic terms representing the behavior of the residuals are interpreted as corrections to the mentioned analytical theories. In particular, the secular rate of the luni-solar inclination of the ecliptic to the equator J2000.0 (–0027, with a mean square error 0000005) is very close to its theoretical value (Williams, 1994).

scholarly journals Application of the Spectral Analysis for Modeling the Rotations of the Moon

2010 ◽  
Vol 45 (4) ◽  
pp. 153-162 ◽  
Author(s):  
V. Pashkevich ◽  
G. Eroshkin
Keyword(s):  
Spectral Analysis ◽  
Numerical Solution ◽  
Rotational Motion ◽  
Initial Conditions ◽  
Analytical Theory ◽  
Time Interval ◽  
The Moon ◽  
Physical Libration ◽  
Newtonian Case ◽  
Rotational Motions

Application of the Spectral Analysis for Modeling the Rotations of the Moon The main purposes of this research are the development of the optimal spectral analysis schemes for the investigation of the rotational motion of the Moon and then the comparison between the result of the optimal spectral analysis of the rotational motions of the Earth and the Moon. Dynamics of the rotational motion of the Moon is studied numerically by using Rodrigues-Hamilton parameters over 418.9 year time interval. The results of the numerical solution of the problem are compared with the composite semi-analytical theory of the Moon rotation (SMR) represented by Cassini relations and the semi-analytical solutions of the lunar physical libration problem (Eckhardt, 1981), (Moons, 1982), (Moons, 1984), (Pešek, 1982). The initial conditions of the numerical integration are taken from SMR. The investigation of the discrepancies is carried out by the optimal spectral analysis methods for the Newtonian case. All the periodic terms representing the behavior of the residuals are interpreted as corrections to SMR semi-analytical theory. As a result, the Moon Rotation Series (MRS2010) is constructed, which is dynamically adequate to the DE200/LE200 ephemeris over 418.9 year time interval. A numerical solution for the Moon rotation is obtained anew with the new initial conditions calculated by means of MRS2010. The discrepancies between the new numerical solution and MRS2010 do not surpass 20 mas over 418.9 year time interval. The result of the comparison demonstrates that MRS2010 series represent more accurately the Moon rotation than SMR series.

scholarly journals Zircon U-Pb and Pyrite Re-Os Isotope Geochemistry of ‘Skarn-Type’ Fe-Cu Mineralization at the Shuikoushan Polymetallic Deposit, South China: Implications for an Early Cretaceous Mineralization Event in the Nanling Range

Minerals ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 480
Author(s):  
Shengbin Li ◽  
Yonghua Cao ◽  
Zeyou Song ◽  
Dan Xiao
Keyword(s):  
Contact Zone ◽  
Early Cretaceous ◽  
South China ◽  
Isotope Geochemistry ◽  
Time Interval ◽  
Mean Square ◽  
Geochronological Data ◽  
Nanling Range ◽  
Calcite Veins ◽  
Os Isotope

The Shuikoushan deposit is an economic ‘skarn-type’ polymetallic Pb-Zn deposit in South China. The deposit is located at the southern margin of the Hengyang basin in the northern part of the Nanling Range. Recently, economic Fe-Cu mineralization that occurs spatially connected to skarns along the contact zone between the granodiorite and limestones was discovered in the lower part of this deposit. Detailed zircon U-Pb geochronological data indicate that the granodiorite was emplaced at 153.7 ± 0.58 Ma (Mean Square of Weighted Deviates (MSWD) = 2.4). However, the pyrite Re-Os isochron age reveals that Fe-Cu mineralization formed at 140 ± 11 Ma (MSWD) = 8.1), which post-dates the emplacement of the granodiorite, as well as the previously determined timing of Pb-Zn mineralization (157.8 ± 1.4 Ma) in this deposit. Considering that Fe-Cu mineralization was connected with the contact zone and also faults, and that sulfide minerals commonly occur together with quartz and calcite veins that crosscut skarns, we interpret this mineralization type as being related to injection of post-magmatic hydrothermal fluids. The timing of Fe-Cu mineralization (140 ± 11 Ma) is inconsistent with a long-held viewpoint that the time interval of 145 to 130 Ma (e.g., Early Cretaceous) in the Nanling Range is a period of magmatic quiescence with insignificant mineralization, the age of 140 Ma may represent a new mineralization event in the Nanling Range.

scholarly journals The wave form of atmospherics at night

1940 ◽  
Vol 176 (965) ◽  
pp. 180-202 ◽  
Keyword(s):  
Wave Form ◽  
Time Interval ◽  
Time Separation ◽  
The Earth ◽  
Lightning Channel ◽  
Reflexion Coefficient ◽  
Primary Pulse

The wave form of all atmospherics received at night from sources within 2000 km. can be accurately described as a ground pulse followed by a series of sky pulses produced by successive reflexions between the ionosphere and the earth, thirty such reflexions being frequently recorded. The time separation between the peaks of these pulses is determined by the distance travelled and the height of the layer. The primary pulse emitted by the source is usually a single complete oscillation of period ranging from 50 to 400//sec. A t distances greater than 500 km. the ground pulse and the first sky pulse merge owing to the shortness of the time interval between them . Differences of amplitude, form and phase between pulses can arise from differences in angle of emission from the parent lightning channel. The height of the reflecting layer can be determined within ± 1 km. It ranged from 85-5 to 90-5 km. during two winter months, with a mean of 88-0 km. The distances of the sources as found by analysis of the pulse series were corroborated by independent location with cathode-ray direction-finders. The reflexion coefficient of the layer for the pulses of longer period exceeded 0-80. The velocity of the ground pulse where it can be tested is within 0.7 % of that of light.

Discrete mean square approximation applied to error calculation in biomolecules and brownian motion

2021 ◽  
Author(s):  
Branislav Randjelovic ◽  
Bojana Markovic ◽  
Vojislav V. Mitic ◽  
Sanja Aleksic ◽  
Dusan Milosevic ◽  
...  
Keyword(s):  
Brownian Motion ◽  
Condensed Matter ◽  
Research Data ◽  
Mean Square ◽  
Fractal Nature ◽  
External Energy ◽  
The Earth ◽  
Whole Space ◽  
Get Complex ◽  
Research Frontiers

Advanced research frontiers are extended from biophysics relations on the Earth upto the discovering any type of alive matter within the whole space. Microorganisms’ motion within the molecular biology processes integrates variety of microorgnisms functions. In continuation of our Brownian motion phenomena research, we consistently build molecular-microorganisms structures hierarchy. We recognize everywhere biomimetic similarities between the particles in alive and nonalive matter. The research data are based on real experiments, without external energy impulses. So, we develop the analysis, inspired by fractal nature Brownian motion, as recognized joint parameter between particles in alive and nonalive biophysical systems. This is also in line with advance trends in hybrid submicroelectronic integrations. The important innovation in this paper is that we introduced approximation of trajectory and error calculations, using discrete mean square approximation, what cumulatively provide much more precise biophysical systems parameters. By this paper, we continue to generate new knowledge in direction to get complex relations between the particles clusters in biophysical systems condensed matter.

ON DESIGNING IMPEDANCE TUBE WITH GRAZING FLOW

Akustika ◽  
2021 ◽  
pp. 80
Author(s):  
Vadim Palchikovskiy ◽  
Igor Khramtsov ◽  
Aleksander Kuznetsov ◽  
Victor Pavlogradskiy
Keyword(s):  
Numerical Simulation ◽  
Analytical Solutions ◽  
Gas Dynamics ◽  
Aircraft Engine ◽  
Design Parameters ◽  
Experimental Setup ◽  
Structural Units ◽  
Impedance Tube ◽  
Acoustic Liners ◽  
Grazing Flow

The article considers the general issues arising in designing the experimental setup “Impedance tube with grazing flow”, the main structural units of the setup, and their purpose. It is given the basic requirements to be provided by the setup when testing samples of acoustic liners used in an aircraft engine. The choosing of the design parameters of the setup is based on the analysis of the known analytical solutions of the acoustics and gas dynamics, and on the numerical simulation of the grazing flow in the impedance tube.

Utilizing the Effort/Motion Approach in the Simulation of Interconnected Rigid Body Systems

1997 ◽  
Author(s):  
N. Duke Perreira
Keyword(s):  
Numerical Simulation ◽  
Rigid Body ◽  
Multibody Systems ◽  
Invariant Form ◽  
Second Law ◽  
Orthogonal Projections ◽  
Gauge Invariant ◽  
Motion Equations ◽  
Newton's Second Law ◽  
Constraint Surface

Abstract The effort/motion approach has been developed for use in designing, simulating and controlling multibody systems. Some aspects of each of these topics are discussed here. In the effort/motion formulation two sets of equations based on the orthogonal projections of a dimensional gauge invariant form of Newton’s Second Law occur. The projections are onto the normal and tangent directions of a dimensional gauge invariant constraint surface. The paper shows how these equations are obtained for a particular linkage with redundant effort and motion actuation. Two alternative Runga-Kutta based approaches for numerical simulation of the effort/motion equations are developed and applied in simulating the motion and determining the effort generated in the example linkage under various conditions. Oscillation about equilibrium positions, solutions with constant motion and with constant effort are given as examples of the approach.

The Earth Sciences and Creative Practice

2015 ◽  
pp. 110-140
Author(s):  
Suzette Worden
Keyword(s):  
Earth Sciences ◽  
Digital Media ◽  
Time Interval ◽  
Audience Participation ◽  
Transdisciplinary Approach ◽  
Deep Time ◽  
Environmental Care ◽  
The Earth ◽  
Geological Age ◽  
Curatorial Practice

The Anthropocene is being suggested as a new geological age replacing the Holocene and is a description of a time interval where significant conditions and processes are profoundly altered by human activity. Artists interested in the earth sciences are using digital media to provide audiences with ways of understanding the issues highlighted in discussions about the Anthropocene. These artists are harnessing data through visualisation and sonification, facilitating audience participation, and are often working in art-science collaborations. These activities demonstrate a transdisciplinary approach that is necessary for confronting the world's most pressing problems, such as climate change. After a discussion of the opportunities provided by visualisation technologies and an overview of the Anthropocene, this chapter explores the following interrelated themes through examples of creative works: (1) nanoscale, (2) geology and deep time, (3) climate, weather, and the atmosphere, (4) extreme places – beyond wilderness, and (5) curatorial practice as environmental care.

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