CMES-Vol. 111, No. 3, 2016

Open Access

ARTICLE

Stable and Minimum Energy Configurations in the Spherical, Equal Mass Full 4-Body Problem
D.J. Scheeres¹
CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.3, pp. 203-227, 2016, DOI:10.3970/cmes.2016.111.203
Abstract The minimum energy and stable configurations in the spherical, equal mass full 4-body problem are investigated. This problem is defined as the dynamics of finite density spheres which interact gravitationally and through surface contact forces. This is a variation of the gravitational n-body problem in which the bodies are not allowed to come arbitrarily close to each other (due to their finite density), enabling the existence of resting configurations in addition to orbital motion. Previous work on this problem has outlined an efficient and simple way in which the stability of configurations in this problem More >

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A Tree-Based Approach for Efficient and Accurate Conjunction Analysis
Michael Mercurio¹, Puneet Singla²
CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.3, pp. 229-256, 2016, DOI:10.3970/cmes.2016.111.229
Abstract Conjunction analysis is the study of possible collisions between objects in space. Conventional conjunction analysis algorithms are geared towards computing the collision probability between any two resident space objects. Currently, there are few heuristic methods available to select which objects should be considered for a detailed collision analysis. A simple all-on-all collision analysis results in an O(N2) procedure, which quickly becomes intractable for large datasets. The main objective of this research work is to preemptively determine which catalogued objects should be considered for a more detailed conjunction analysis, significantly reducing the number of object pairs More >

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Continued Fraction Cartesian to Geodetic Coordinate Transformation
J.D. Turner¹ , A. Alnaqeb¹, A. Bani Younes¹
CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.3, pp. 257-268, 2016, DOI:10.3970/cmes.2016.111.257
Abstract A singularity-free perturbation solution is presented for inverting the Cartesian to Geodetic transformation. Conventional approaches for inverting the transformation use the natural ellipsoidal coordinates, this work explores the use of the satellite ground-track vector as the differential correction variable. The geodetic latitude is recovered by well-known elementary means. A high-accuracy highperformance 3D vector-valued continued fraction iteration is constructed. Rapid convergence is achieved because the starting guess for the ground-track vector provides a maximum error of 30 m for the satellite height above the Earth's surface, throughout the LEO-GEO range of applications. As a result, a More >

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Solution of Liouville's Equation for Uncertainty Characterization of the Main Problem in Satellite Theory
Ryan Weisman³, Manoranjan Majji⁴, Kyle T. Alfriend⁵
CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.3, pp. 269-304, 2016, DOI:10.3970/cmes.2016.111.269
Abstract This paper presents a closed form solution to Liouville's equation governing the evolution of the probability density function associated with the motion of a body in a central force field and subject to J2. It is shown that the application of transformation of variables formula for mapping uncertainties is equivalent to the method of characteristics for computing the time evolution of the probability density function that forms the solution of the Liouville's partial differential equation. The insights derived from the nature of the solution to Liouville's equation are used to reduce the dimensionality of uncertainties More >

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