Juan F. Navarro

A New Symbolic Processor for the Earth Rotation Theory

In this paper we present a new symbolic processor specially suited for the Earth rotation theory. This processor works with a more general kind of Poisson series called Kinoshita series, which has resulted to be very useful in the Earth rotation theory. Its structure is adapted for dealing with the more general analytical expressions that appear in the Earth rotation theory. This new algebraic processor has been successfully used for computing different contributions to the nutation series of the rigid Earth.

On the implementation of the Poincaré-Lindstedt technique

Abstract The aim of this paper is to present a new algebraic processor which implements the basic algebra of modified quasipolynomials, including routines to compute the solution to a linear second-order differential equation presenting undetermined coefficients. The kernel of this algebraic system is a very useful tool for a generic implementation of the Poincare–Lindstedt method to find periodic solutions in slightly perturbed systems.

Computation of periodic solutions in perturbed second-order ODEs

Abstract The Poincare–Lindstedt technique is used to compute periodic solutions in perturbed ordinary differential equations. In this paper, we give a general algorithm for its application on a special purpose symbolic computation package.

The Asymptotic Expansion Method via Symbolic Computation

This paper describes an algorithm for implementing a perturbation method based on an asymptotic expansion of the solution to a second-order differential equation. We also introduce a new symbolic computation system which works with the so-called modified quasipolynomials, as well as an implementation of the algorithm on it.

Consistency Problems in the Improvement of the IAU Precession–Nutation Theories: Effects of the Dynamical Ellipticity Differences

The complexity of the modeling of the rotational motion of the Earth in space has produced that no single theory has been adopted to describe it in full. Hence, it is customary using at least a theory for precession and another one for nutation. The classic approach proceeds by deriving some of the fundamental parameters from the precession theory, like, e.g., the dynamical ellipticity

Spiral Structures and Chaotic Scattering of Coorbital Satellites

H_{\mathrm{d}}

Principal Matrix of a Linear System Symbolically Computed

Hd, and then using those values in the nutation theory. The former IAU 1976 precession and IAU 1980 nutation theories followed that scheme. Along with the improvement of the accuracy of the determination of Earth orientation parameters, IAU 1980 was superseded by IAU2000, based on the application of the MHB2000 transfer function to the previous rigid Earth analytical theory REN2000. The latter was derived while the precession model IAU 1976 was still in force, therefore it used the corresponding values for some of the fundamental parameters, as the precession rate, associated to the dynamical ellipticity. The new precession model P03 was adopted as IAU 2006. That change introduced some inconsistency since P03 used different values for some of the fundamental parameters that MHB2000 inherited from REN2000. Besides, the derivation of the basic Earth parameters of MHB2000 itself comprised a fitted variation of the dynamical ellipticity adopted in the background rigid theory. Due to the strict requirements of accuracy of the present and coming times, the magnitude of the inconsistencies originated by this twofold approach is no longer negligible as earlier, hence the need of discussing the effects of considering slightly different values for