Application of the Nonrestricted Three-Bodies Problem to the Stellar System ξ UMa

The present study concerns the application of an analytical theory of the stellar three- - bodies problem to the triple stellar system ξ UMa, whose components move along short-period orbits with periods of 2 years and 60 years. For this purpose the solution of the simplified canonical system of differential equations obtained in terms of hyperelliptic integrals by Hamilton-Jacobi method was used. The precision of the solution was increased by addition of short-periodic terms computed from the formulae of the transformation by von Zeipel’s method.