Methods of Celestial Mechanics: Volume I: Physical, Mathematical, and Numerical Principles
Springer Science & Business Media, 18.11.2004 - 466 sivua
G. Beutler's Methods of Celestial Mechanics is a coherent textbook for students as well as an excellent reference for practitioners. The first volume gives a thorough treatment of celestial mechanics and presents all the necessary mathematical details that a professional would need. The reader will appreciate the well-written chapters on numerical solution techniques for ordinary differential equations, as well as that on orbit determination. In the second volume applications to the rotation of earth and moon, to artificial earth satellites and to the planetary system are presented. The author addresses all aspects that are of importance in high-tech applications, such as the detailed gravitational fields of all planets and the earth, the oblateness of the earth, the radiation pressure and the atmospheric drag. The concluding part of this monumental treatise explains and details state-of-the-art professional and thoroughly-tested software for celestial mechanics.
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Overview of the Work
The ComputerProgram ERDROT
The Equations of Motion
The Two and the ThreeBody Problems 123
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accuracy algorithm angular momentum argument of latitude assume boundary value problem celestial body Celestial Mechanics center of mass Chapter circular orbit coefficients collocation epochs collocation method components computed condition equations coordinate system corresponding defined derivatives w.r.t. differential equation system dynamical Earth rotation eccentricity elliptic eqns equations of motion Euler Figure ﬁrst formula Gaussian geocentric geodesy gravitational inertial system initial epoch initial value problem integration interval Jupiter Kepler’s linear combination matrix mean anomaly minor planet multistep methods numerical solution observations obtained orbit determination orbit improvement orbital elements orbital motion orbital plane order q osculating elements osculating orbital PAI-system partial derivatives pericenter perturbation equations planetary system point masses polynomial position vector procedure referring result right-hand side rounding errors scalar semi-major axis solution vector solved stepsize subinterval t(years Table three-body problem tion transformation true anomaly two-body problem variational equations velocity vector