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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