Error propagation in the numerical solutions of the differential equations of orbital mechanics

Details Error propagation in the numerical solutions of the differential equations of orbital mechanics Error propagation in the numerical solutions of the differential equations of orbital mechanics

May 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..27...65b&link_type=abstract

Celestial Mechanics, vol. 27, May 1982, p. 65-77.

Physics

Differential Equations, Encke Method, Error Analysis, Numerical Integration, Numerical Stability, Orbital Mechanics, Cartesian Coordinates, Circular Orbits, Eccentric Orbits, Eigenvalues, Finite Element Method, Runge-Kutta Method, Two Body Problem

Scientific paper

The relationship between the eigenvalues of the linearized differential equations of orbital mechanics and the stability characteristics of numerical methods is presented. It is shown that the Cowell, Encke, and Encke formulation with an independent variable related to the eccentric anomaly all have a real positive eigenvalue when linearized about the initial conditions. The real positive eigenvalue causes an amplification of the error of the solution when used in conjunction with a numerical integration method. In contrast an element formulation has zero eigenvalues and is numerically stable.

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