We study the dynamics of a particle moving under gravitation of precessing dynamically symmetric rigid body if the particle motion is restricted by two unilateral (flexible) constraints realized by two weightless unstretchable tethers with ends fixed at body poles, formed as the intersection of the body surface with the axis of its dynamical symmetry. The system under consideration is a simple model of an original natural-artificial space construction consisting of an asteroid and a space station tethered to each other via two cables. We note that the problem is integrable for the system safe configurations, i.e. for motions along the constraints common boundary (both tethers are tensed) if the body gravitational potential is invariant with respect to rotation about the axis of dynamical symmetry. We study these motions depicting phase portraits for possible values of system parameters. We also deduce conditions for the particle coming off the boundary of constraint(s) (if the tether(s) are slackened) and analyze these conditions, eliminating corresponding areas from phase portraits. We also formulate some statements, concerning the particle safety.
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