Aerospace Instrument-Making Annotation << Back A FORMATION OF THE PROGRAM MOTION OF n BODIES ENSEMBLE S.N. Chukanov The problem of comparing the initial and target form of an ensemble of n bodies, which is the grouping of spacecrafts, is considered. To analyze the deformations of the shape of the ensemble of n bodies, method of groups of diffeomorphisms is used. The problem is solved on the basis of the method for constructing the minimized functional characterizing the evolution of the transformation of the ensemble form from the initial to the terminal, and the penalty for deviating the trajectory of the bodies from the required trajectory. The formulation of the problem based on the construction and solution of Hamilton’s equations for the group of diffeomorphisms of particles – points of landmark of the image is given. An algorithm for solving Hamilton’s equations for a diffeomorphic transformation is developed based on the stochastic gradient descent method. Key words: ensemble n bodies, Hamilton equation, stochastic gradient descent, diffeomorphic transformation. Contacts: E-mail: ch_sn@mail.ru Pp. 22-27.