The principle of virtual work and Lagrange’s equations of motion are used to construct a system of differential equations for constrained spatial multibody system modeling. The differential equations are augmented with algebraic constraints representing the system being modeled. The resulting system is a high index differential-algebraic equation (DAE) which is cast as an ordinary differential equation (ODE) by differentiating the constraint equations twice. The initial conditions are the heliocentric rectangular equatorial generalized coordinates and their first time derivatives of the planets of the solar system and an artificial satellite. The ODE is computed using the integration subroutine LSODAR to generate the body generalized coordinates and time derivatives and hence produce the planetary ephemerides and satellite trajectories for a time interval. Computer simulation and graphical output indicate the satellite and planetary positions and the latter may be compared with those provided in the Astronomical Almanac. Constraint compliance is investigated to establish the accuracy of the computation. [S0021-8936(00)03403-6]
Numerical Computation of Differential-Algebraic Equations for the Approximation of Artificial Satellite Trajectories and Planetary Ephemerides
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, March 31, 1999; final revision, May 5, 1999. Associate Technical Editor: A. A. Ferri. Discussion on the paper should be addressed to the Technical Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
Fox, B., Jennings, L. S., and Zomaya, A. Y. (May 5, 1999). "Numerical Computation of Differential-Algebraic Equations for the Approximation of Artificial Satellite Trajectories and Planetary Ephemerides ." ASME. J. Appl. Mech. September 2000; 67(3): 574–580. https://doi.org/10.1115/1.1313820
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