FA-69638 / Orbital propagation / Member archive

Stumpff functions for universal variables: Series branch is used far from zero · case 03

Moderate z values lose accuracy in the truncated series.

Member previewVariant 3 · 3 implementations · 7 checks per implementation

Case contract

Input z. For z>1e-6: C=(1-cos s)/z, S=(s-sin s)/s^3 with s=sqrt z; for z<-1e-6: C=(cosh s-1)/(-z), S=(sinh s-s)/s^3 with s=sqrt(-z); otherwise series C=1/2-z/24+z^2/720, S=1/6-z/120+z^2/5040. Return [C,S] rounded to 10.

Why this case matters

Orbit determination and mission planning chain many small conversions; one wrong branch or unit silently moves a spacecraft by kilometres.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
stumpff functions for universal variables 0.05	`[0.4979201389, 0.166250496]`	`[0.4979201358, 0.1662504957]`	Failed

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