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Added Zeis model for DSST J2-squared second order terms.

Merged Bryan Cazabonne requested to merge issue-931 into develop

Addition of the Zeis model for J2-squared second order terms used in DSST.

I tested using 3 different orbits: very-LEO, LEO, and MEO (Lageos 2). For the 3 cases, using J2-squared improve the accuracy of the DSST propagation compared to the numerical method by a factor 3 (see the three test cases in DSSTJ2SquaredClosedFormTest). I implemented the field methods and validated the computation of the derivatives.

I performed a more detailed analysis of these 3 test cases: plots are below.

Num_vs_DSST_wo_J2Squared

Num_vs_DSST_with_J2Squared

Because the mean to osculating (and inverse) transformation doesn't exist yet, even using the new feature the difference between DSST and numerical is not equal 0.0. Indeed, currently J2-Squared is only used in the mean elements integration. I suppose the short period terms could also have a significant impact, but they don't exist in the literature yet.

Issue #931 (closed)

Edited by Bryan Cazabonne