A third-order solution of Vinti's problem with explicit expressions for the poisson brackets

We have derived an explicit third-order solution of Vinti's problem including J₃. Poisson brackets for the elements a, e, s, M_s, ψ_s and $\text{Ω}{}_{\mathrm{s}}$ are given. These may be used in the construction of a third-order theory of artificial satellites.