Osculating lattice paths are sets of directed lattice paths which are not allowed to cross or have common edges, but are allowed common vertices. We derive a constant term formula for the number of such lattice paths. The formula is obtained by solving a set of simultaneous recurrence relations. Alternating sign matrices are in simple bijection with a subset of osculating lattice paths. This le...

Abstract The merits of a perturbation theory based on mean-to-osculating transformation that is purely periodic in the fast angle are investigated. exact separation perturbed Keplerian dynamics into short-period effects and long-period mean frequencies achieved by non-canonical transformation, which, therefore, cannot be obtained Hamiltonian methods. For this case, evolution elements strictly a...

Both orbital and attitude dynamics employ the method of variation of parameters. In a non-perturbed setting, the coordinates (or the Euler angles) are expressed as functions of the time and six adjustable constants called elements. Under disturbance, each such expression becomes ansatz, the "constants" being endowed with time dependence. The perturbed velocity (linear or angular) consists of a ...

Discussion of different types of osculating orbital elements for motion of real dust particle under the action of electromagnetic radiation in the central gravitational field is presented. It is shown that physically correct access is based on gravitational acceleration as the only radial acceleration – " radiation pressure " is not included in the radial acceleration.