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A second order secular J-S planetary theory. Part I, Lemma

Kamel O. M., Soliman A. S.

Mechanics and Mechanical Engineering

2018

Vol. 22, nr 4

871--874

A concise lemma is given for the construction of a semi-analytic Hamiltonian second order secular J-S planetary theory using the Jacobi-Radau system of origins and in terms of the non-singular variables of H. Poincaré. We truncate our expansions at the desired power in the eccentricities and the sines of the inclinations.

A Semi-Analytic First Order Jupiter-Saturn Planetary Theory. Part II

Kamel O. M., Soliman A. S.

Mechanics and Mechanical Engineering

2016

Vol. 20, nr 3

233--247

In this part we present the algebraic calculus computations related to the Hamiltonian equations of motion for the Jupiter – Saturn subsystem. Also we give a comment on the methods of the solution for the system of linear and nonlinear differential equations describing the motion of this subsystem.