English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper compares the continuum evolution for density equation modellingand the Gaussian mixture model on the 2D phase space long-term densitypropagation problem in the context of high-altitude and high area-to-mass ratiosatellite long-term propagation. The density evolution equation, a purenumerical and pointwise method for the density propagation, is formulated underthe influence of solar radiation pressure and Earth's oblateness usingsemi-analytical methods. Different from the density evolution equation andMonte Carlo techniques, for the Gaussian mixture model, the analyticalcalculation of the density is accessible from the first two statistical moments(i.e., the mean and the covariance matrix) corresponding to each sub-Gaussiandistribution for an initial Gaussian density distribution. An insight is giveninto the phase space long-term density propagation problem subject to nonlineardynamics. The efficiency and validity of the density propagation aredemonstrated and compared between the density evolution equation and theGaussian mixture model with respect to standard Monte Carlo techniques.

Comparison of continuity equation and Gaussian mixture model for long-term density propagation using semi-analytical methods