Passing through resonance: The excitation and dissipation of the lunar free libration in longitude

1993 ◽  
Vol 57 (1-2) ◽  
pp. 307-324 ◽  
Author(s):  
Donald H. Eckhardt
Keyword(s):  
Free Libration

scholarly journals Planetary and Earth Figure Perturbations in the Librations of the Moon

1981 ◽  
Vol 63 ◽  
pp. 193-198
Author(s):  
Donald H. Eckhardt
Keyword(s):  
The Moon ◽  
Free Libration ◽  
Analytic Models

AbstractComparisons of numeric, semi-analytic and analytic lunar libration models indicate that the planetary and Earth figure perturbations used to supplement the semi-analytic and analytic models are inadequate. Using the ELP-2000 of Chapront and Chapront-Touzé, an improved solution of these perturbations is developed. For the libration in longitude there are numerous terms with periods near that of the free libration; their amplitudes remain ill-defined.

Effects of a physical librations of the moon caused by a liquid core, and determination of the fourth mode of a free libration

2014 ◽  
Vol 48 (6) ◽  
pp. 403-419 ◽  
Author(s):  
Yu. V. Barkin ◽  
H. Hanada ◽  
K. Matsumoto ◽  
S. Sasaki ◽  
M. Yu. Barkin
Keyword(s):  
Liquid Core ◽  
The Moon ◽  
Free Libration ◽  
Fourth Mode

scholarly journals Theory of Motion of Jupiter’s Galilean Satellites

1978 ◽  
Vol 41 ◽  
pp. 207-207
Author(s):  
J.H. Lieske
Keyword(s):  
Analytic Functions ◽  
Digital Computer ◽  
Algebraic Manipulation ◽  
Physical Parameters ◽  
Galilean Satellites ◽  
Partial Derivatives ◽  
Theory Of Motion ◽  
Analytic Expressions ◽  
Free Libration ◽  
Future Revision

AbstractThe final results for the theory enabling one to calculate the positions of the Galilean satellites and their partial derivatives are presented, following the techniques outlined in earlier papers. Extensive use of algebraic manipulation software on a digital computer is employed to generate the final expressions. The new theory is, in effect, a revitalization of Sampson’s theory in which we (a) remove algebraic and mathematical errors existing in Sampson’s work, (b) introduce some neglected effects due to solar interactions and the 3-7 commensurability, (c) allow for non-zero amplitude and phase of the free libration, (d) express the final results as analytic functions of variations in 49 arbitrary constants of integration and physical parameters, (e) construct the theory in a manner which readily allows for future revision, and (f) provide analytic expressions for the partial derivatives with respect to the 49 parameters.

scholarly journals Hamiltonian Theory of the Libration of the Moon

1978 ◽  
Vol 41 ◽  
pp. 125-135 ◽  
Author(s):  
Jacques Henrard ◽  
Michèle Moons
Keyword(s):  
Perturbation Technique ◽  
Mean Value ◽  
Canonical Transformations ◽  
The Moon ◽  
Physical Libration ◽  
Transform Method ◽  
Lie Transform ◽  
Hamiltonian Theory ◽  
The Mean ◽  
Free Libration

AbstractThe feasibility of applying the Lie transform method to the problem of the physical libration of the Moon is investigated. By a succession of canonical transformations, the Hamiltonian of the problem is brought under a form suitable for perturbation technique. The mean value of the inclination of the angular momentum upon the ecliptic and the frequencies of the free libration are computed.

On the possible amplitudes of the moon's free libration

The Moon ◽  
1970 ◽  
Vol 2 (1) ◽  
pp. 78-93 ◽  
Author(s):  
N. Sekiguchi
Keyword(s):  
Free Libration

scholarly journals Complements to Moons’ Lunar Libration Theory

1999 ◽  
Vol 172 ◽  
pp. 317-328
Author(s):  
J. Chapront ◽  
M. Chapront-Touzé ◽  
G. Francou
Keyword(s):  
Frequency Analysis ◽  
Tidal Effects ◽  
Periodic Perturbations ◽  
Numerical Integrations ◽  
Free Libration

AbstractAnalytical complements have been brought to Moons’ lunar libration theory concerning tidal effects, direct perturbations due to the Earth’s figure, and indirect non periodic perturbations. Comparisons to JPL numerical integrations DE245 and DE403 have been performed and the residuals treated by frequency analysis, allowing the determination of fitted free libration parameters and numerical complements.

Estimation of the lunar free libration modes based on the recent ephemerides

2019 ◽  
Vol 364 (12) ◽  
Author(s):  
Yongzhang Yang ◽  
Qingbao He ◽  
Jinsong Ping ◽  
Jianguo Yan ◽  
Wenzhao Zhang
Keyword(s):  
Free Libration

scholarly journals Estimation of the Lunar Physical Librations

1997 ◽  
Vol 165 ◽  
pp. 21-30 ◽  
Author(s):  
X X Newhall ◽  
J. G. Williams
Keyword(s):  
Fourier Analysis ◽  
Least Squares ◽  
Estimation Procedure ◽  
Least Squares Estimation ◽  
Time Varying ◽  
Free Libration

AbstractThe recent long-term integration of JPL ephemeris DE403/LE403 yielded lunar physical librations covering 6000 years. A Fourier analysis of a 718-year subset of this span produced estimates of the component frequencies of the forced and free librations. A subsequent iterative least-squares estimation procedure provided precise values for phases and for time-varying amplitudes and frequencies. Two free libration modes were found; presence of a third is possible but close to the noise.

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