## On constructing the Earth' rotation theory in the trigonometrical form

Transactions of IAA RAS, issue 21, 145–152 (2010)

**Keywords**:
Земли, методом общей планетной теории GPT, короткопериодические члены, долгопериодические члены, эволюция орбит, эволюционные переменные, квазипериодический коэффициент, решение SMART97

### Abstract

In the present paper the equations of the orbital motion of the major planets and the Moon and the equations of the three-axial rigid Earth's rotation in Euler parameters are reduced to the secular system describing the evolution of the planetary and lunar orbits (independent of the Earth's rotation) and the evolution of the Earth's rotation (depending on the planetary and lunar evolution). Hence, the theory of the Earth's rotation can be presented by means of the series in powers of the evolutionary variables with quasi-periodic coefficients with respect to the planetary-lunar mean longitudes. This form of the Earth's rotation problem is compatible with the general planetary theory involving the separation of the short--period and long--period variables and avoiding the appearance of the non-physical secular terms. The approximate numerical estimates of the constants of the secular system solution are obtained by comparing it with the classical SMART97 solution. The results in $\dot\phi$, $\dot\theta$, $\dot\psi$ coincide up to 10/d for the epoch J2000

### Citation

`V. Brumberg, T. Ivanova. On constructing the Earth' rotation theory in the trigonometrical form // Transactions of IAA RAS. — 2010. — Issue 21. — P. 145–152.`

```
@article{brumberg2010,
abstract = {In the present paper the equations of the orbital motion of the major planets and the Moon and the equations of the three-axial rigid Earth's rotation in Euler parameters are reduced to the secular system describing the evolution of the planetary and lunar orbits (independent of the Earth's rotation) and the evolution of the Earth's rotation (depending on the planetary and lunar evolution). Hence, the theory of the Earth's rotation can be presented by means of the series in powers of the evolutionary variables with quasi-periodic coefficients with respect to the planetary-lunar mean longitudes. This form of the Earth's rotation problem is compatible with the general planetary theory involving the separation of the short--period and long--period variables and avoiding the appearance of the non-physical secular terms. The approximate numerical estimates of the constants of the secular system solution are obtained by comparing it with the classical SMART97 solution. The results in $\dot\phi$, $\dot\theta$, $\dot\psi$ coincide up to 10/d for the epoch J2000},
author = {V. Brumberg and T. Ivanova},
issue = {21},
journal = {Transactions of IAA RAS},
keyword = {Земли, методом общей планетной теории GPT, короткопериодические члены, долгопериодические члены, эволюция орбит, эволюционные переменные, квазипериодический коэффициент, решение SMART97},
pages = {145--152},
title = {On constructing the Earth' rotation theory in the trigonometrical form},
url = {http://iaaras.ru/en/library/paper/713/},
year = {2010}
}
```

```
TY - JOUR
TI - On constructing the Earth' rotation theory in the trigonometrical form
AU - Brumberg, V.
AU - Ivanova, T.
PY - 2010
T2 - Transactions of IAA RAS
IS - 21
SP - 145
AB - In the present paper the equations of the orbital motion of the major
planets and the Moon and the equations of the three-axial rigid
Earth's rotation in Euler parameters are reduced to the secular
system describing the evolution of the planetary and lunar orbits
(independent of the Earth's rotation) and the evolution of the
Earth's rotation (depending on the planetary and lunar evolution).
Hence, the theory of the Earth's rotation can be presented by means
of the series in powers of the evolutionary variables with quasi-
periodic coefficients with respect to the planetary-lunar mean
longitudes. This form of the Earth's rotation problem is compatible
with the general planetary theory involving the separation of the
short--period and long--period variables and avoiding the appearance
of the non-physical secular terms. The approximate numerical
estimates of the constants of the secular system solution are
obtained by comparing it with the classical SMART97 solution. The
results in $\dot\phi$, $\dot\theta$, $\dot\psi$ coincide up to 10/d
for the epoch J2000
UR - http://iaaras.ru/en/library/paper/713/
ER -
```