Abstract
The purpose of this chapter is to remind the reader of the basics of mathematics and mechanics, which are necessary for understanding the material presented in subsequent chapters. The coordinate systems and transition matrices used in the book are described. The two-body problem is considered, and the equations of motion in an unperturbed Keplerian orbit are obtained. Planetary equations for perturbed motion are written in the Gauss and Lagrange form. The main orbital perturbing forces and torques are considered. The equations of relative motion of one body in the orbital coordinate system of another body are obtained in the simplest spacecraft formation flight statement, and the equations of a rigid body attitude motion are written for a noninertial reference frame. The main theorems of the Lyapunov stability theory are given. Finally, the chapter describes the construction of Poincare sections and the calculation of the Lyapunov exponents spectrum for the analysis of chaotic motions.
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