Introduction to the application of von zeipel's method
Application of von zeipel method to satellite orbiting under gravitational field influence and perturbations due to earth oblateness
GRAVITATIONAL FIELD↗
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Notes on von zeipel's method
Canonical problems and von zeipel method - theory and application
VON ZEIPEL METHOD↗
On Von Zeipel's method in general planetary theory
Von Zeipel method in general planetary theory
PLANETARY MOTION↗
On the elimination of the short period terms of a first order general planetary theory through Von Zeipel's method
Elimination of short period terms of first order general planetary theory through Von Zeipel method
VON ZEIPEL METHOD↗
On a generalization of the elimination of the short period terms of a first order general planetary theory through Von Zeipel's method and Hori canonical variables
Elimination of short period terms of first order general planetary theory through Von Zeipel method and Hori canonical variables
Meffroy, J.↗
Modified long-period behavior due to tesseral harmonics.
Von Zeipel method and Hamiltonian perturbation mechanics used for orbits at resonance with tesseral harmonics of geopotential
GEOPOTENTIAL↗
The motion of a satellite in resonance with the longitude-dependent harmonics
The solution to the motion of a satellite in an eccentric orbit and in resonance with one or more of the longitude-dependent harmonics of the central planet is developed. The method of solution parallels the well known von Zeipel method of general perturbations. The solution consists of expressions for the variations of the Delaunay variables. These expressions are composed of the perturbations developed by Brouwer in 1959 for the motion of an artificial satellite plus first-order resonant perturbations due to longitude-dependent harmonics (in terms of Legendre normal elliptic integrals of the first and second kind).
Dallas, S. S.↗
The motion of a satellite in resonance with the longitude-dependent harmonics
The solution to the motion of a satellite in an eccentric orbit and in resonance with one or more of the longitude-dependent harmonics of the central planet is developed. The method of solution parallels the well known von Zeipel method of general perturbations. The solution consists of expressions for the variations of the Delaunay variables. These expressions are composed of the perturbations developed by Brouwer in 1959 for the motion of an artificial satellite plus first-order resonant perturbations due to longitude-dependent harmonics (in terms of Legendre normal elliptic integrals of the first and second kind).
Dallas, S. S.↗
The motion of a satellite in resonance with the second-degree sectorial harmonic
The solution to the motion of a satellite in an eccentric orbit and in resonance with the second-degree sectorial harmonic of the potential field is developed. The method of solution used parallels the well known von Zeipel method of general perturbations. The solution consists of expressions for the variations of the Delaunay variables. These expressions are composed of the perturbations developed by Brouwer in 1959 for the motion of an artificial satellite plus first-order perturbations due to the second-degree sectorial harmonic (in terms of the Legendre normal elliptic integrals of the first and second kind).
Dallas, S. S.↗
COMPARISON OF THE VON ZEIPEL AND MODIFIED HANSEN METHODS AS APPLIED TO ARTIFICIAL SATELLITES
Application of von zeipel and modified hansen methods to artificial satellite orbit calculations
VON ZEIPEL METHOD↗
Rigorous error bounds on position and velocity in satellite orbit theories.
Rigorous error bounds on position and velocity of satellite derived from Hamiltonian theory and von Zeipel method
HAMILTONIAN↗
Rigorous error bounds on position and velocity in satellite orbit theories.
Rigorous error bounds on position and velocity of satellite derived from Hamiltonian theory and von Zeipel method
ELLIPTICAL ORBIT↗
On the perturbations of small-eccentricity satellites
Perturbation theory for artificial satellites with nearly circular orbits using Von Zeipel method
Felsentreger, T. L.↗
Modified long-period behavior due to tesseral harmonics.
Von Zeipel method and Hamiltonian perturbation mechanics used for orbits at resonance with tesseral harmonics of geopotential
Vagners, J.↗
A new formulation of canonical perturbation theory
Modification of Poincare-Von Zeipel method for canonical perturbation theory
Stern, D. P.↗
A new formulation of canonical perturbation theory
Canonical perturbation theory formulation applied to Poincare-von Zeipel method
Stern, D. P.↗
Long period perturbations of earth satellite orbits
All the equations involved in extending the PS phi solution to include the long periodic and second order secular effects of the zonal harmonics are presented. Topics covered include DSphi elements and relations for their conconical transformation into the PS phi elements; the solution algorithm based on the Von Zeipel method; and the elimination of long periodic terms and analytical integration of primed variables. The equations were entered into the ASOP program, checked out, and verified. Comparisons with numerical integrations show the long period theory to be accurate within several meters after 800 revolutions.
Wang, K. C.↗
Computation of Hansen coefficients
Some procedures are presented for computer development of Hansen coefficients. The method of Von Zeipel and Andoyer was found to be most efficient. A table extends the method from 7th to 12th order.
Cherniack, J. R.↗