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Epicycles and Poincar\'{e} Resonances in General Relativity
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Epicycles and Poincar\'{e} Resonances in General Relativity
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The method of geodesic deviations provides analytic approximations to geodesics in arbitrary background space-times. As such the method is a useful tool in many practical situations. In this note we point out some subtleties in the application of the method related to secular motions, in first as well as in higher order. In particular we work out the general second-order contribution to bound orbits in Schwarzschild space-time and show that it provides very good analytical results all the way up to the innermost stable circular orbit.
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Cited by 1 Pith paper
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Geodesic deviation to all orders via a tangent bundle formalism
A tangent-bundle flow formalism yields an explicit all-orders formula for the Jacobi propagators in geodesic deviation, with the Lagrangian and equation of motion given explicitly up to tenth order.
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