A multi-segment alpha shape-based continuum method for long-term density propagation with bifurcation

This paper studies the bifurcation case for the planar phase space long-term density propagation problem, and presents an improved multi-segment continuum method for accurate and efficient long-term density propagation, by introducing the multi-segment method to the alpha shape triangulation-based linear interpolation method. The density evolution equation is formulated for the continuum density propagation under the influence of the solar radiation pressure and Earth’s oblateness using semi-analytical equations. For the overall highly deformed and elongated density distribution for the bifurcation case, the multi-segment method is introduced to the alpha shape-based linear interpolation method to get accurate interpolated density, by dividing the overall density distribution into multiple segments and performing the linear interpolation within the actual non-convex hull of the sample distribution for each segment. Four segments are divided for the overall density distribution considering the Hamiltonian dynamic constraints on the solar angle domain. The superiority of the improved multi-segment alpha shape-based continuum method is demonstrated for accurate and efficient density propagation for the bifurcation case in the context of the high-altitude and high area-to-mass ratio satellite long-term propagation.