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Relativistic rotation of the rigid body in the Rodrigues-Hamilton parameters: Lagrange function and equations of motion

Pashkevich V. V., Eroshkin G. I.

Artificial Satellites : Journal of Planetary Geodesy

2018

Vol. 53, No. 3

89--115

The main purposes of this research are to obtain Lagrange function for the relativistic rotation of the rigid body, which is generated by metric properties of Riemann space of general relativity and to derive the differential equations, determining the rigid body rotation in the terms of the Rodrigues-Hamilton parameters. The Lagrange function for the relativistic rotation of the rigid body is derived from the Lagrange function of the nonrotation point of masses system in the relativistic approximation.

MRS2016: rigid Moon Rotation Series in the relativistic approximation

Pashkevich V. V.

Artificial Satellites : Journal of Planetary Geodesy

2017

Vol. 52, No. 1

1--8

The rigid Moon rotation problem is studied for the relativistic (kinematical) case, in which the geodetic perturbations in the Moon rotation are taken into account. As the result of this research the high-precision Moon Rotation Series MRS2016 in the relativistic approximation was constructed for the first time and the discrepancies between the highprecision numerical and the semi-analytical solutions of the rigid Moon rotation were investigated with respect to the fixed ecliptic of epoch J2000, by the numerical and analytical methods. The residuals between the numerical solution and MRS2016 in the perturbing terms of the physical librations do not exceed 80 mas and 10 arc seconds over 2000 and 6000 years, respectively.