Segmentation of the spacecraft transfer problem through overdetermined and continuity constraints based on the Theory of Functional Connections

For the three-segment case with support functions s1=(1,t,t^2), s2=(1,t), s3=(1,t,t^2) and the eight combined constraints, the paper gives explicit constrained functionals (its Eq. (14)) that contain 1/13 coefficients. Solving the same eight-by-eight linear system directly yields a different, uniquely determined solution with determinant 8 T^3 and coefficients built from 1/8, 1/4, etc. The two cannot both be correct. A simple counterexample (all g-values and their derivatives set to zero, vi=vf=0) shows the paper’s r1(t) t^2-coefficient equals 3(rf−ri)/(13 T^2) whereas the correct value from the linear system is (rf−ri)/(4 T^2), proving the paper’s expression is wrong. The model’s derivation matches the structure rn=gn+En sn, the constraints, and recovers the published Ns=2 formula (paper’s Eq. (10)), but disagrees with the Ns=3 formula (Eq. (14)). Therefore, the model is correct and the paper’s Ns=3 explicit expression is in error.