For every bounded trajectory of a particle in an arbitrary central field of force a uniformly rotating reference frame may be chosen in which this trajectory becomes closed. This circumstance makes it meaningful to introduce a nonconserving analog of the Runge-Lenz-Laplace vectorA called the «precession vector» here and to build theSO4 Poisson-bracket algebra with it. The corresponding hidden symmetry is minimally broken in the sense that the vectorA keeps its length constant and rotates with constant angular speed. In the present paper the phase space of the bounded motions in the 3-dimensional central problem is canonically mapped into a product of two three-dimensional spheres in a four-dimensional space each, and theSO4 acts linearly by rotations on them. The Hamiltonian formalism in this curved phase manifold is obtained. The particle moves with a constant speed along a diametral circle, this circle precessing with a constant angular speed.