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In this paper we present a framework which provides an analytical (i.e., infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the gravitational two-body problem. The formalism omits all singular variables which otherwise would yield discontinuities. This method is based on two simple real functions for which the derivative rules are only required to be known, all other applications -- e.g., calculating the orbital velocities, obtaining the partial derivatives of radial velocity curves with respect to the orbital elements -- are thereafter straightforward. As it is shown, the presented formalism can be applied to find optimal instants for radial velocity measurements in transiting exoplanetary systems to constrain the orbital eccentricity as well as to detect secular variations in the eccentricity or in the longitude of periastron.
Implementing the modal method in the electromagnetic grating diffraction problem delivered by the curvilinear coordinate transformation yields a general analytical solution to the 1D grating diffraction problem in a form of a T-matrix. Simultaneously
The isentropic vortex problem is frequently solved to test the accuracy of numerical methods and verify corresponding code. Unfortunately, its existing solution was derived in the relativistic magnetohydrodynamics by numerically solving an ordinary d
We apply moment methods to obtaining an approximate analytical solution to Knudsen layers. Based on the hyperbolic regularized moment system for the Boltzmann equation with the Shakhov collision model, we derive a linearized hyperbolic moment system
Analytical solutions in fluid dynamics can be used to elucidate the physics of complex flows and to serve as test cases for numerical models. In this work, we present the analytical solution for the acoustic boundary layer that develops around a rigi
Paper is published in J. Phys. A: Math. Theor. 43 (2010) 225001, doi:10.1088/1751-8113/43/22/225001. Exact analytical solution for the universal probability distribution of the order parameter fluctuations as well as for the universal statistical and