Ever see the ill-fated “DID NOT CONVERGE” message when using the differential corrector profile in a Target Sequence in Astrogator? Maybe you ran the Mission Control Sequence (MCS) again and thankfully it converged, or maybe you ran it multiple times, all to no avail… Sometimes the selected dependent variables (equality constraints or results) just aren’t good enough for the Target Sequence to converge. Some orbital elements are not smooth functions and can cause the differential corrector to jump back and forth around a solution.
Some of the most common issues occur when targeting the following:
- Zero Eccentricity
- Zero or X Inclination
- Zero Eccentricity and Zero Inclination together
- Converting an Impulsive Burn Solution to a Finite Burn
The picture below demonstrates a case where a spacecraft is transferred from LEO to GEO but the differential corrector has difficulty driving the eccentricity to zero within the specified tolerance.
In this case, eccentricity is a rough function because of the way it approaches zero from one side (it's impossible to have a negative eccentricity). This makes iterative methods messier and can sometimes lead to a non-convergent solution. To help drive the eccentricity to zero, flight-path angle is added as an additional constraint since we know that a circular orbit will have a zero flight-path angle at every point along the orbit. Targeting both zero eccentricity and zero flight-path angle helps the Target Sequence converge more easily!
You may be wondering about how to deal with the other common issues mentioned. Have no fear… we have good news here! We have already created a brief FAQ article and a white paper that takes an in-depth look at these common issues and what their respective solutions are.