Astronomy and Astrophysics – Astronomy
Scientific paper
Jun 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003scchg..46..307w&link_type=abstract
Science in China Series G: Physics, Mechanics and Astronomy, Volume 46, Issue 3, pp.307-320
Astronomy and Astrophysics
Astronomy
Perturbation Theory, Elastic Bodies, Euler Variation, Post-Newtonian Approximation
Scientific paper
In this paper the dynamical equations for an elastic deformable body in the first post-Newtonian approximation of Einstein theory of gravity are derived in rotating spherical coordinates. The unperturbed rotating body (the relaxed ground state) is described as uniformly rotating, stationary and axisymmetric configuration in an asymptotically flat space-time manifold. Deviations from the equilibrium configuration are described by means of a displacement field. By making use of the schemes developed by Damour, Soffel and Xu, and by Carter and Quintana we calculate the post-Newtonian Lagrangian strain tensor and symmetric trace-free shear tensor. Considering the Euler variations of Einstein’s energy-momentum conservation law, we derive the post-Newtonian energy equation and Euler equations of elastic deformable bodies in rotating spherical coordinates.
Michael Soffel
Wu Xue-jun
Xu Chong-ming
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