Particularities of the application of the equations of motion in gravitational fields in nonlinear problems to problems, when equations or solutions contain nonsmooth functions, are discussed. Classical mechanics is engaged in the study of properties, approximation and prediction of motion for problems with regular functions. Solving nonlinear equations of dynamics uses additional transformations to eliminate singularities of equations for complex systems that lead to a linear or simplified form. This gives the possibility of solving with regard to the stages of successive approximation. The application of such transformations is considered for solving the problems of controlled motion of space vehicles in the gravitational field, taking into account active and reactive forces. After reduction to the canonical form or regular elements of nonlinear equations of dynamics we obtain the initial approximation. The control by the relay view determines the switching times at corner points based on the Pontryagin maximum principle. It is required to join successive sections of the trajectory.