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Abstract: The effect of initial and couple stresses on the propagation and attenuation of seismic body waves in a dissipative orthotropic medium is considered. In the limiting cases, the phase velocities of P-wave and SV-wave along coordinate axes are deduced. The study shows that the presence of compressive initial stresses increases the velocity of longitudinal wave (P-wave) but diminishes that of transverse wave (SV-wave). It also observed that the loss of longitudinal wave due to dissipation is maximum in the initially stress-free case and decreases as the initial stress increases. In the case of transverse wave, the presence of initial stresses decreases the loss factor up to the point of when the direction of propagation makes an angle of 40° with direction of initial stress, and then increases. It can be concluded that both the velocities and attenuations depend on not only the material constants but also on the initial stresses present in the medium and the direction of wave propagation. Also, it has been shown that the couple stress has no effect on both velocities and attenuations of seismic waves propagating in this medium. [Copyright &y& Elsevier]

Abstract: The eigenvalue approach, using the Laplace and Fourier transforms, has been employed to find the analytical expressions for displacements and stresses at any point, as a result of an inclined line load, of an initially stressed orthotropic elastic medium. A plain strain problem has been studied. The results in the form of displacement and stress components have been obtained and discussed graphically for a particular model. In this paper it is shown that the displacement and stress components are affected by initial stresses in the medium. [Copyright &y& Elsevier]

Abstract: The present work deals with the encounter problem of two small masses m 2 and m 3 describing initially elliptical orbits around a massive oblate primary. The equations of motion are developed, up to the power of the small parameter, both for the center of mass and for the relative motion of m 2 and m 3 without any restrictions on the orbital elements. The equations of motion of the center of mass are expressed in terms of the Struble variables. [Copyright &y& Elsevier]

The critical inclination problem in artificial satellite theory and the post-Newtonian (PN) effects on it are discussed. The Hamiltonian is constructed and is expressed in terms of the Delaunay variables containing the zonal harmonics up to J4 and the PN contributions up to order J2/cl2. The Hamiltonian is ordered out such that the PN terms are of order J2. Two successive canonical transformations based on Lie series and transform are carried out to remove short- and long-period terms from the Hamiltonian, respectively. Terms are retained up to third order in the secular and to the second order in the periodic terms, where J2 is considered of first order. [Copyright &y& Elsevier]

The critical inclination problem in artificial satellite theory and the post-Newtonian (PN) effects on it are discussed. The Hamiltonian is constructed and is expressed in terms of the Delaunay variables containing the zonal harmonics up to J4 and the PN contribution up to order J2/cl2. The Hamiltonian is ordered out such that the PN terms are of order J2. Two successive canonical transformations based on Lie series and transform are carried out to remove short and long period terms from the Hamiltonian, respectively. Terms are retained up to the third order in the secular perturbations and to the second order in the periodic perturbations, where J2 is considered of first order. [Copyright &y& Elsevier]

Abstract: Working with the mean orbit elements, the secular drift of the longitude of the ascending node and the sum of the argument of perigee and mean anomaly are set equal between two neighboring orbits. By having both orbits drift at equal angular rates on the average, they will not separate over time due to the influence of the perturbative effects of the asphericity of the Earth, as is considered in this work. The problem is stated. The expressions for the time rate of change of the longitude of the ascending node and the sum of the argument of perigee and mean anomaly in terms of the Delaunay canonical elements are obtained. The expressions for the second order conditions that guarantee that the drift rates of two neighboring orbits are equal on the average are derived. [Copyright &y& Elsevier]