Numerical Stabilization of Orbital Motion

Mainly, the author focuses on Baumgarte's method and its applications in satellite, asteroid, stellar and planetary problems. In the paper arguments are given for the use of energy relations for stabilization in the elliptical two-body problem. Stabilizing properties of Baumgarte's equations and others are discussed. A simple approach is proposed for stabilizing the equations of almost circular motion. By using Baumgarte's technique, the author derives stabilized equations of perturbed restricted three-body problem. It is shown experimentally that stabilization in the problems mentioned above can raise the accuracy of numerical integration by several orders.     

Coronal Holes and Icosahedral Symmetry

The study of the expansion of the solar wind out of a system of coronal holes is continued. To this end, we consider the numerical integration of partial differential equations for problems with icosahedral symmetry, in general. First, employing Weyl theory, orbifold coordinates are introduced. Second, the icosahedral coordinates are discussed in detail. Third, following an analysis of the properties of these coordinates and the derivation of a few expressions useful for grid construction, various alternatives for the distribution of lattice points required for numerical integration are considered. A comparison of these numerical grids motivates the choice of a specific grid optimized for the numerical integration carried out in the accompanying paper by Kalish et al.(2002). This revised version was published online in July 2006 with corrections to the Cover Date.