Internal links in the Earth-Moon system are determined by gravitational interaction. According to the least compulsion principle of Gauss, the deviation of “free motion” of heliocentric orbits of two material points with Earth and Moon masses is determined by the sum of the products of each material points’ deviation from its free motion and its mass.

By solving the minimization problem using the Lagrange multiplier method, Lagrange equations of the first kind were obtained in vector form. With acceptable assumptions (introduction of non-dimensional time τ = nt, where n is the sidereal rotation of the Moon, and the lunar orbit is considered to be circular) the linkage coefficient (Lagrange multiplier) is:

where v1and v2 are proper frequencies of the Earth and the Moon and μ is the Moon/Earth mass ratio.