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 Construction of the New High-Precision Moon Rotation Series at a Long Time Intervals

2011 ◽  
Vol 46 (2) ◽  
pp. 63-73
Author(s):  
V. Pashkevich ◽  
G. Eroshkin
Keyword(s):  
Numerical Solution ◽  
High Precision ◽  
Initial Conditions ◽  
Analytical Theory ◽  
Time Interval ◽  
The Moon ◽  
Time Intervals ◽  
Good Consistency ◽  
Newtonian Case ◽  
Long Time

Construction of the New High-Precision Moon Rotation Series at a Long Time Intervals The main purposes of this research are the construction of the new high-precision Moon Rotation Series (MRS2011), dynamically adequate to the DE404/LE404 and the DE406/LE406 ephemeris, over long time intervals. The comparison of the new highprecision Moon Rotation solutions of MRS2011 with the solution of MRS2010 (Pashkevich and Eroshkin, 2010), which is dynamically adequate to the DE200/LE200 ephemeris over 418.9 year time interval, is performed. The dynamics of the rotational motion of the Moon is studied numerically by using Rodrigues-Hamilton parameters over 418.9, 2000 and 6000 years. The numerical solution of the Moon rotation is implemented with the quadruple precision of the calculations. The results of the numerical solution of the problem are compared with the composite semi-analytical theory of the Moon rotation (SMR) (Pashkevich and Eroshkin, 2010) with respect to the fixed ecliptic of epoch J2000. The initial conditions of the numerical integration are taken from SMR. The investigation of the discrepancies is carried out by the least squares and spectral analysis methods for the Newtonian case. All the secular, periodic and Poisson terms, representing the behavior of the residuals, are interpreted as corrections to SMR semi-analytical theory. As a result, the Moon Rotation Series (MRS2011) is constructed, which is dynamically adequate to the DE404/LE404 and the DE406/LE406 ephemeris over 418.9, 2000 and 6000 years. A numerical solution for the Moon rotation is obtained anew with the new initial conditions calculated by means of MRS2011. The discrepancies between the new numerical solution and the semi-analytical solution of MRS2011 do not surpass 20 mas over 418.9 year time interval, 64 mas over 2000 year time interval and 8 arc seconds over 6000 year time interval. Thus, the result of the comparison demonstrates a good consistency of MRS2011 series with the DE/LE ephemeris.

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 Smallest Chimeras Under Repulsive Interactions

2021 ◽  
Vol 1 ◽  
Author(s):  
Suman Saha ◽  
Syamal Kumar Dana
Keyword(s):  
Rotational Motion ◽  
Initial Conditions ◽  
Stability Function ◽  
Chimera State ◽  
The Third ◽  
Periodic State ◽  
Repulsive Interactions ◽  
Librational Motion ◽  
Rotational Motions ◽  
Pass Through

We present an exemplary system of three identical oscillators in a ring interacting repulsively to show up chimera patterns. The dynamics of individual oscillators is governed by the superconducting Josephson junction. Surprisingly, the repulsive interactions can only establish a symmetry of complete synchrony in the ring, which is broken with increasing repulsive interactions when the junctions pass through serials of asynchronous states (periodic and chaotic) but finally emerge into chimera states. The chimera pattern first appears in chaotic rotational motion of the three junctions when two junctions evolve coherently, while the third junction is incoherent. For larger repulsive coupling, the junctions evolve into another chimera pattern in a periodic state when two junctions remain coherent in rotational motion and one junction transits to incoherent librational motion. This chimera pattern is sensitive to initial conditions in the sense that the chimera state flips to another pattern when two junctions switch to coherent librational motion and the third junction remains in rotational motion, but incoherent. The chimera patterns are detected by using partial and global error functions of the junctions, while the librational and rotational motions are identified by a libration index. All the collective states, complete synchrony, desynchronization, and two chimera patterns are delineated in a parameter plane of the ring of junctions, where the boundaries of complete synchrony are demarcated by using the master stability function.

Use of an Analytical Theory for the Physical Libration of the Moon to Detect Free Nutation of the Lunar Core

2018 ◽  
Vol 62 (12) ◽  
pp. 1021-1025 ◽  
Author(s):  
N. K. Petrova ◽  
Yu. A. Nefedyev ◽  
A. A. Zagidullin ◽  
A. O. Andreev
Keyword(s):  
Analytical Theory ◽  
The Moon ◽  
Physical Libration ◽  
Free Nutation ◽  
Lunar Core

scholarly journals Relativistic aspects of rotational motion of celestial bodies

2009 ◽  
Vol 5 (S261) ◽  
pp. 112-123 ◽  
Author(s):  
S. A. Klioner ◽  
E. Gerlach ◽  
M. H. Soffel
Keyword(s):  
High Precision ◽  
Rotational Motion ◽  
Earth Rotation ◽  
Theoretical Framework ◽  
Reference Systems ◽  
The Moon ◽  
Newtonian Theory ◽  
Recent Developments ◽  
Celestial Bodies ◽  
Near Future

AbstractRelativistic modelling of rotational motion of extended bodies represents one of the most complicated problems of Applied Relativity. The relativistic reference systems of IAU (2000) give a suitable theoretical framework for such a modelling. Recent developments in the post-Newtonian theory of Earth rotation in the limit of rigidly rotating multipoles are reported below. All components of the theory are summarized and the results are demonstrated. The experience with the relativistic Earth rotation theory can be directly applied to model the rotational motion of other celestial bodies. The high-precision theories of rotation of the Moon, Mars and Mercury can be expected to be of interest in the near future.

scholarly journals Numerical solution for consistent initial conditions of constrained mechanical systems

2003 ◽  
Vol 25 (3) ◽  
pp. 170-185
Author(s):  
Dinh Van Phong
Keyword(s):  
Numerical Solution ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Flexible Approach ◽  
Constrained Mechanical Systems ◽  
Consistent Initial Values

The article deals with the problem of consistent initial values of the system of equations of motion which has the form of the system of differential-algebraic equations. Direct treating the equations of mechanical systems with particular properties enables to study the system of DAE in a more flexible approach. Algorithms and examples are shown in order to illustrate the considered technique.

scholarly journals MINERAL MAPPING USING CHANDRAYAAN-1 HYPERSPECTRAL (HYSI) DATA FROM MARE VAPORUM

2018 ◽  
Vol XLII-5 ◽  
pp. 339-344
Author(s):  
S. B. Sayyad ◽  
Z. R. Mohammed ◽  
R. R. Deshmukh
Keyword(s):  
Spectral Analysis ◽  
Lunar Surface ◽  
Imaging Spectroscopy ◽  
The Moon ◽  
Remotely Sensed Data ◽  
Mineral Mapping ◽  
Crustal Composition ◽  
False Color ◽  
Color Composite ◽  
Surface Mineralogy

<p><strong>Abstract.</strong> The imaging spectroscopy offers an opportunity to map and discriminate different minerals on the lunar surface which further helps to understand the origin, evolution process, and the crustal composition on the surface of the moon. Compositional mapping of the lunar surface is considered as a standard approach for mineral mapping. This paper reports surface mineralogy of the lunar surface from Mare Vaporum using Chandrayaan-1 Hyperspectral remotely sensed data from HySi sensor. False color composite is created using different band shaping algorithms like band strength; band curve and band tilt parameters at crucial wavelength for spatial analysis. The Spectral analysis has been done by deriving reflectance spectra at varying locations from the area under study. The Study shows the mineral map with different categories of minerals which are high-Ca pyroxene and/or olivine and low Ca-pyroxene. However because of the limited spectral coverage of HySi, data at the longer wavelengths required to discriminate among different group of minerals.</p>

ON THE JOINT APPLICATION OF THE COLLOCATION BOUNDARY ELEMENT METHOD AND THE FOURIER METHOD FOR SOLVING PROBLEMS OF HEAT CONDUCTION IN FINITE CYLINDERS WITH SMOOTH DIRECTRICES

2021 ◽  
pp. 15-38
Author(s):  
D.Y. Ivanov ◽  
Keyword(s):  
Fourier Series ◽  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Initial Conditions ◽  
Fourier Method ◽  
Time Interval ◽  
Cylindrical Domain ◽  
Two Dimensional ◽  
Element Method

Here we consider the initial-boundary value problems in a homogeneous cylindrical domain YI Ω ×+ ( Ω+ is an open two-dimensional bounded simply connected domain with a boundary 5 ∂Ω ∈C , 2 \ Ω≡ Ω − + R is the open exterior of the domain Ω+ , [0, ] YI ≡ Y is the height of the cylinder) on a time interval [0, ] TI ≡ T . The initial conditions and the boundary conditions on the bases of the cylinder are zero, and the boundary conditions on the lateral surface of the cylinder are given by the function 1 2 wx x yt ( , , ,) ( 1 2 (, ) x x ∈∂Ω , Y y ∈ I , T t I ∈ ). An approximate solution of such problems is obtained through the combined use of the Fourier method and the collocation boundary element method based on piecewise quadratic interpolation (PQI). The solution to the problem in the cylinder is expanded in a Fourier series in terms of eigenfunctions of the operator 2 By yy ≡ ∂ with the corresponding zero boundary conditions. The coefficients of such a Fourier series are solutions of problems for two-dimensional heat equations 2 2 t ∇ =∂ + u u ku . With a low smoothness of the functions w in the variable y, the weight of solutions at large values of k increases and the accuracy of solving the problem in the cylinder decreases. To maintain accuracy on a uniform grid, the step of discretization of the boundary function w with respect to the variable y is decreased by a factor of j. Here j is an averaged value of the quantity Y k π depending on the function w. In addition, the steps of discretization of functions ( ) 2 exp − τ k with respect to the variable τ in domains τ≤πT k are reduced by a factor of 2 2 k π . The steps in the remaining ranges of values τ and the steps by the other variables remain unchanged. The approximate solutions obtained on the basis of this procedure converge stably to exact solutions in the 2 ( ) LI I Y T × -norm with a cubic velocity uniformly with respect to sets of functions w, bounded by norm of functions with low smoothness in the variable y, uniformly along the length of the generatrix of the cylinder Y , and uniformly in the domain Ω . The latter is also associated with the use of PQI along the curve ∂Ω over the variable 2 2 ρ≡ − r d , which is carried out at small values of r ( d and r are the distances from the observed point of the domain Ω to the boundary ∂Ω and to the current point of integration along ∂Ω , respectively). The theoretical conclusions are confirmed by the results of the numerical solution of the problem in a circular cylinder, where the dependence of the boundary functions w on y is given by the normalized eigenfunctions of the differential operator By which vary in a sufficiently large range of values of k .

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