Nonsingular Euler Parameterizations for Motion of a Point Mass in Atmospheric Flight

The paper explicitly derives the rv–Euler ODEs and notes they remain well defined at the vertical–downward configuration εB1 = ηB = 0, thereby eliminating the vertical–flight singularity that plagues spherical azimuth dynamics; the paper also exhibits the spherical azimuth rate with 1/cosγ and tanγ terms, which is undefined at γ = ±90° (Eq. 69) . The candidate solution reaches the same conclusions by systematically listing all denominators in the rv–Euler right‑hand sides (m, r, r^2, m v) and verifying they are nonzero on r>0, v>0, while pointing out the spherical azimuth singularity via the explicit factors 1/cosγ and tanγ. The paper further states rvh–Euler is singular at Eh = r×v = 0 and rvL–Euler removes the bank angle while remaining nonsingular, which aligns with the candidate’s optional discussion .