Construction of an equivalent system of equations of motion of a dynamically compressed satellite relative to its center of mass

The restricted problem of the motion of a dynamically symmetrical compressed satellite relative to its center of mass in a circular orbit in the earth's gravitational field is examined. The use of the k-squared(t) amplitude function and a known Jacobi integral makes it possible to reduce the initial system of Euler-Poinsot equations to a 3rd-order system of special form, describing the change of nutation and precession angles. At k-squared(t) = (k sub 0)-squared = const, the solution is determined in elliptic functions, which makes possible a simple choice of the reference solution for the construction of a solution using the method of successive approximations.