An overview of new directions in modern celestial mechanics is given. The starting point is the Gaussian ring, the gravitational potential of which is obtained in analytical form. Instead of osculating Keplerian elements, a set of new variables is introduced: these are the Laplace and Hamilton vectors, as well as the vector of the orbital angular momentum of the body. In the linear approximation, the evolution equations in new variables are obtained, replacing the classical Lagrange equations. The method is tested on the exosystem HD 206893. The problem of confinement of rings around small celestial bodies is considered. Two new approaches based on two-dimensional (R-disk) and three-dimensional (R-toroid) generalizations of precessing Gauss rings are presented. The methods are tested by solving problems on the dynamics of stellar rings in the Galaxy and the secular evolution of orbits in various exoplanet systems.