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The hyperbolic encounter of compact objects results burst like gravitational wave signal. We analyze the motion of spinning binary systems with the construction of a general parametrization of the radial motion which is valid for all types of the orbits. With the time dependence of the parameter the gravitational waveforms can be constructed.
Recently we derived the next-to-next-to-leading order post-Newtonian Hamiltonians at spin-orbit and spin(1)-spin(2) level for a binary system of compact objects. In this talk the derivation of them will be shortly outlined at an introductory level. We will also discuss some checks of our (complicated and long) results in the first part of the talk. In the second part we will show how to apply our results to the calculation of the last stable circular orbit of such a binary system of black holes or neutron stars.