The theoretical standard for finding the stability of a rocket is the Barrowman Equations, first derived by the husband and wife team of James and Judith Barrowman in 1966 while they worked at NASA. The original paper provided the first theoretical characterization of the stability of a rocket. By applying a large number of simplifications the original equations can be significantly simplified and all calculus eliminated from the process. Further work during the 90's extended the Barrowman equations into large angle of attack situations, as well as incorporating viscous effects and non-linear aerodynamic theory, developed during the preceding 30 years.
Original Paper:
Extended Barrowman Method: