  Novel method for semi-analytical solving of equations of a trapped dynamics
for a planetoid m4 close to the plane of mutual motion of main bodies around
each other (in case of a special type of Bi-Elliptic Restricted 4-Bodies
Problem) is presented. We consider here three primaries m1, m2, m3 orbiting
around their center of mass on elliptic orbits which are permanently forming
Lagrangian configuration of an equilateral triangle. Our aim is to obtain
appoximate coordinates of quasi planar trajectory of the infinitesimal
planetoid m4, when the primaries have masses equal to 1/3. Results are as
follows: 1) equations for coordinates {x, y} are described by system of coupled
2-nd order ordinary differential equations with respect to true anomaly f, 2)
expression for z stems from solving second order Riccati ordinary differential
equation that determines the quasi-periodical oscillations of planetoid m4 not
far from invariant plane {x, y, 0}.
