Related papers: Analytic Solution for Perturbed Keplerian Motion U…
The dynamics of small global perturbations in the form of linear combination of a finite number of non-axisymmetric eigenmodes is studied in two-dimensional approximation. The background flow is assumed to be an axisymmetric perfect fluid…
We give an overview of basic methods that can be used for obtaining asymptotic expansions of integrals: Watson's lemma, Laplace's method, the saddle point method, and the method of stationary phase. Certain developments in the field of…
The orbital motion of a binary system is characterized by various characteristic temporal intervals which, by definition, are different from each other: the draconitic, anomalistic and sidereal periods. They all coincide in the Keplerian…
Stars near the Galactic center reach a few percent of light speed during pericenter passage, which makes post-Newtonian effects potentially detectable. We formulate the orbit equations in Hamiltonian form such that the $O(v^2/c^2)$ and…
We propose a new approach to Bayesian prior probability distributions (priors) that can improve orbital solutions for low-phase-coverage orbits, where data cover less than approximately 40% of an orbit. In instances of low phase coverage…
We present a method to find asymptotics for the evolution of coherent states (or Gaussian wavepackets with standard deviation $\sqrt{h}$) under semiclassical Schr\"odinger's equation for a given Hamiltonian. These results extend the work of…
The transport of high-energy particles in the presence of small-scale, turbulent magnetic fields is a long-standing issue in astrophysics. Analytical theories on transport perpendicular to the large-scale magnetic field disagree with…
In this work, we study the motions in the region around the equilateral Lagrangian equilibrium points L4 and L5, in the framework of the Circular Planar Restricted Three-Body Problem (hereafter, CPRTBP). We design a semi-analytic approach…
Planet-planet perturbations can cause planets' orbital elements to change on secular timescales. Previous work has evaluated the nodal precession rate for planets in the limit of low $\alpha$ (semi-major axis ratio, 0$<$$\alpha$$\leq$1).…
This paper introduces a novel method for the automatic detection and handling of nonlinearities in a generic transformation. A nonlinearity index that exploits second order Taylor expansions and polynomial bounding techniques is first…
The observation data for artificial celestial body 43096, which had been obtained during 2006-2012 within the framework of international project "The Scientific Network of Optical Instruments for Astrometric and Photometric Observations" -…
We present a systematic study on linear propagation of ultrashort laser pulses in media with dispersion, dispersionless media and vacuum. The applied method of amplitude envelopes gives the opportunity to estimate the limits of slowly…
We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…
This paper presents a simple approach to low-thrust optimal-fuel and optimal-time transfer problems between two elliptic orbits using the Cartesian coordinates system. In this case, an orbit is described by its specific angular momentum and…
An asymptotic investigation of monochromatic electromagnetic fields in a layered periodic medium is carried out under the assumption that the wave frequency is close to the frequency of a stationary point of the dispersion surface. We find…
Based on the Taylor expansion, we propose a renormalization method for asymptotic analysis. The standard renormalization group (RG) method for asymptotic analysis can be derived out from this new method, and hence the mathematical essence…
Bayesian learning is often hampered by large computational expense. As a powerful generalization of popular belief propagation, expectation propagation (EP) efficiently approximates the exact Bayesian computation. Nevertheless, EP can be…
Low Earth orbit (LEO) satellites offer a promising alternative to global navigation satellite systems for precise positioning; however, their relatively low altitudes make them more susceptible to orbital perturbations, which in turn…
The asymptotic expansion method is generalized from the periodic setting to stationary ergodic stochastic geometries. This will demonstrate that results from periodic asymptotic expansion also apply to non-periodic structures of a certain…
We present an efficient and simple modification of the standard transport algorithm used in explicit eulerian fixed polar grid codes, aimed at getting rid of the average azimuthal velocity when applying the Courant condition. This results…