Found a new case of integrability of differential equations of rotational motion of a rigid body about the center of mass in a Central Newtonian field cha- gathania. The case of integrability of the obtained for an axisymmetric rigid body, the principal Central moments of inertia which are connected by equality A = B = 2C, and x(C) = 0, y(C) = 0, z(C) = 0, where C is the center of mass of a rigid body. With exactly the same distribu- tion of mass C. V. Kovalevskaya was solved another problem of rotation of a rigid body around a fixed point in a homogeneous field of gravity. A common solution in this case was recorded in hyperelliptic functions. This decision was received in 1889 Fixed point was located in the Equatorial plane, i.e. x(G) not equal 0, y(G) not equal 0, z(G) not equal 0, where G is the point of application of force of gravity. It turned out that this problem is closely connected with many topical problems of mathematics and mechanics and every year are increasing theoretical and practical application of the results and methods, which they obtained [1]. In our problem, in contrast to the task C. V. Kovalevskaya, Central, regarding which comes rotational motion, combined with the center of mass of the body, consequently, the time of gravity about the center of mass is equal to zero, and the movement of the body occurs in the Central Newtonian gravitational field.
