On the planar inertial motion of a system of three coupled bodies

Numerous papers are devoted to studying the motion of a system (coupling) of two bodies in the Earth’s satellite orbit ([1–4] and others). The problem on the planar inertial motion of three bodies, coupled by a non-extensible weightless string having the form of an unfastened chain, is considered in the paper. Such a configuration can be represented, for example, by a system of two coupled spacecraft rotating around their common center of mass (in order to simulate the gravity force) in long-term space missions, when the third body (the lift) is located on a connecting cable. The bodies are considered to be the material points (particles).     

Some new applications of the generalized problem of two fixed centers

A generalized problem of two fixed centers and its limiting version is considered. New possible applications of this problem are obtained. Using a symmetric version of the problem, the external field of gravitation is approximated. The limiting version approximates the inner field.     

Navigation of a space bunch under conditions of its rotary motion

The properties of a tethered space system (bunch) in the mode of rotational motion are used in determination of the parameters of the location and orientation of the end vehicles of the bunch by the method with the simplest possible instrumental implementation.     

The motion of a particle in perturbed field of an attracting center

The integrable case of the perturbed two-body problem is considered. The perturbation is determined by the potential of a special form. The L-matrix is chosen in such a way that partial separation of variables should take place in regular coordinates. Integration of the equations of motion of the problem under consideration is made. The solutions are expressed through elliptic functions. The orbits for various cases are constructed. The results of numerical calculations are given.     

Planar inertial motion of an elastic cluster of three bodies

A problem of planar inertial motion of three bodies connected in the form of a triangle by an elastic imponderable filament is considered, as well as a particular case of the problem of motion of a closed chain of n bodies. This configuration can be a basis for extended planar constructions in deep space.The bodies are considered as material points. The paper elaborates a subject of [1]     

Determination of two Satellites’ relative motion using tracking measurements

A technique to determine the initial relative velocity of two satellites at the initial time instant, based on the results of NORAD system’s measurements, is presented. The determination of a relative initial position is shown to result in the unsatisfactory accuracy. This technique is applied to determining the initial velocity of separation of the first Russian nanosatellite TNS-0 from the International Space Station.