The equations of motion of an artificial satellite in nonsingular variables

Program KMEC (Kozai Mean Element Converter): The Computation of Kozai Mean Orbital Elements Using a Nonsingular Formulation

“…This is converted in the PFS to the. Brouwer mean semimajor axis a" via the transformation 17 3 4 ''-…”

Long-Period Variations of the Eccentricity Vector Valid also for Near Circular Orbits around a Non-Spherical Body

“…We begin with writing the geopotential and the Lagrange equations with respect to the non-singular elements for eccentricity. Several authors have already expressed the Lagrange equations in non-singular elements: for example (Giacaglia, 1977;Nacozy and Dallas, 1977;Wytrzyszczak, 1986). Here, we write the equations again not only to be self-consistent, but also to give an explicit expression of the coefficients involved in the expansion as power series of the eccentricity of the main differential system.…”

Advanced orbit propagation methods applied to asteroids and space debris

“…- (78) This set only presents a singularity for i " 180˝, a case that is often not interesting for practical applications. The expression for the osculating equations of motion in Lagrange form is provided by Giacaglia [42]. Letting γ " ?…”

“…In the practical calculation of the A i,1 , we have to take into account their dependence from the total disturbing function R " R C`R 1 . After eliminating the short-periodic terms included in their expansions by setting q " 2p´l, we plug them in Equation 95 [42]:…”

“…We show the equations of motion for the set of equinoctial elements E as presented by Giacaglia [42] and Nacozy and Dallas [74], which is expressed in terms of the classical orbital elements as We recall that the components of the incoming (pre-encounter) asymptotic velocity U " v Ast´vC in the pX, Y, Zq frame defined in subsection 3.1.1 are defined by the quantities U, θ, φ:…”