Effect of plane gravitational waves on a system of free particles

The behaviour of two infinitely close test particles in a field of weak plane gravitational waves is investigated. The equations of deviation of geodesies for two particular cases of metric corresponding to two different polarization states is integrated. Two physically different cases are distinguished: (1) the particles are at rest in the laboratory frame of reference; (2) the particles have a nonzero velocity. Three-dimensional Xsup(ij); Ysup(ijk), and Zsup(ikej) tensors are considered as the wave functions of the gravitation - inertial field of the system chosen. Since only the Xsup(ij) and Ysup(ijk) tensors can be assumed independent in vacuum, gravitational waves of two types, X and Y are distinguished. It is noted that if the particles are at rest in the laboratory frame of reference, only X-type gravitational waves may be detected from their relative acceleration, and only by a detector from free masses. If the velocity of the particles is different from zero in the laboratory frame of reference, both X- and Y-type waves can be detected from their relative acceleration, both by a detector from free masses and by a resonance-type detector. Equations expressing the effect of X-type waves on the relative shift of the particles and the general effect of X- and Y-type waves are obtained