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Русская версия

**I. I. Cosenco**

Moscow State University of Services

Glavnaya Str., 99,Cherkizovo-1,Pushkino District

Moscow Region, 141221, Russia

For the case of planar oscillations of a satellite, which moves on elliptic orbit the procedures to prolong continuously solutions to ODE system depending on specified parameter up to its limit value are under consideration. Singularity of ODE occurs when parameter is equal to its limit value. Eccentricity of the orbit is assumed to be the parameter specified. Unit is its singular value and corresponds to the case of parabolic orbit. Application of integral metric with weight functions in the space of phase variables derivatives, namely tangent space plays regularizing role in the procedures cited. To represent the solution approximately it is possible to use Fourier series in corresponding Hilbert space. Coefficients of these series continuously depend on the parameter on the set of all its admissible values, including singular one. Simultaneously the uniform approximation of phase space variables functions with respect to independent variable on any compact set without points of right hand sides functions discontinuities, when the parameter is of its singular value is automatically guaranteed.