In this post, we will see the book by Ye. N. Polyakhova titled *Collection of Problems on the Dynamics of a Point in a Central Force Field.*

## About the book

The collection is a detailed selection of problems on the dynamics of the motion of a material point acted on by a central gravitational force, in particular, the dynamics of space flight. As an exception, the book presents several problems on the motion of a point acted on central non-gravitational forces. The book is written mainly for correspondence students. Topics covered include Kepler’s laws, the integral of areas, Binet’s formulas for central forces, the energy balance and velocity along a space trajectory, time of motion along a space trajectory, conditions for the existence of elliptical trajectories, transfer from orbit to orbit, sphere of action, third escape velocity problems, two-body problem, and the generalized third law of Kepler, along with miscellaneous problems.

This collection is a textbook for the course of theoretical mechanics (“Point Dynamics” section). students in correspondence departments of Leningrad State University and other higher educational institutions used in part by students in the day and evening departments. Moreover, the problem book may prove useful for beginning instructors in providing practical exercises mechanics, particularly, when they prepare modifications of test problems.

Most of the collection is a detailed sampling of problems on the dynamics of a material point acted on by gravitational force, in particular, problems on the elementary dynamics of space flight. Several problems on the motion of a point acted on by central non-gravitational forces are presented. Altogether, the collection includes about 200 problems of varying degrees of difficulties, with solutions.

Translation of *Sbornik zadach po dinamike tochki v pole tsentral’nykh sil,* Leningrad, Leningrad University Press, 1974, pp. 1-145. The book was published by NASA in May 1975 under its technical translation programme (NASA TT F-16,263).

## Contents

Foreword iv

Table of Contents vi

Chapter One. Central Forces. Force of Gravity and Its Dynamic Characteristics 1

Chapter Two. Kepler’s Laws 11

Chapter Three. Integral of Areas 19

Chapter Four. Binet’s Formulas for Central Forces 26

Chapter Five. Energy Balance and Velocity Along a Space Trajectory 36

Chapter Six. Time of Motion in a Space Trajectory 63

Chapter Seven. Conditions for the Existence of Elliptical Trajectories 77

Chapter Eight. Transfer from Orbit to Orbit 90

Chapter Nine. Sphere of Action. Problems of Third Escape Velocity 109

Chapter Ten. Two-Body Problem. Third Kepler’s Law Generalized 118

Chapter Eleven. Miscellaneous Problems 127

References 163