# Rocket Dynamics

## Dynamics, Rocket

the science of the motion of aircraft equipped with reaction engines. The most important characteristic of the flight of a rocket with an operating (thrust-generating) engine is the considerable change in mass during its motion because of the combustion of fuel. Single-stage rockets lose up to 90 percent of their initial (launch) mass in the process of acceleration. The laws of motion of a rocket with an operating engine are given by the equations of the mechanics of bodies of variable mass.

The theoretical foundations of rocket dynamics were laid by the works of the Russian scientists I. V. Meshcherskii and K. E. Tsiolkovskii at the turn of the 20th century. The rapid development of the science began after World War II (1939-45) in connection with the growth of rocket construction in the industrially developed countries (the USSR, the USA, and France).

The most important branches of rocket dynamics are the study of the motion of the center of mass (center of gravity) of rockets—that is, the establishment of a theory devoted to the solution of trajectory problems of rocket dynamics; the study of the motion of rockets relative to the center of mass, in which problems of stabilization, the possibilities of maneuvering and control and guidance to a given target, as well as docking of spacecraft with rocket engines in orbit in outer space, are studied; and experimental rocket dynamics, in which research is done on experimental methods for the study of rocket motion. Optical and radio devices are widely used to determine the geometric, kinematic, and dynamic characteristics of the flight, which determine both the motion of the rocket’s center of mass and motion relative to the center of mass.

A unique class of problems in rocket dynamics is caused by the necessity for programming the magnitude and direction of thrust in order to produce from the quantity of propellant (fuel and oxidizer) available the optimum flight characteristics for reaching the target (for example, maximum flight range, minimum flight time to the target, and maximum kinetic energy at the end of engine operation). Such problems are successfully solved by methods of the calculus of variations and promote the development of these very methods. New branches of rocket dynamics, which study the motion of the rocket hull, taking into account the oscillation of the liquid propellant in its tanks and the motion of the rocket as an elastic body, are being successfully developed in connection with the construction of very large liquid-fuel rockets. These new problems are so complex that they cannot be studied analytically. Digital computers are used to solve such problems (multiparameter problems).

In the dynamics of guided missiles (for example, antiaircraft and antimissile missiles), some of the external influences are probabilistic in nature and are quantitatively determined by “random” functions of time. The solution of these problems requires the use of the theory of probabilistic processes.

### REFERENCES

*Kosmicheskaia tekhnika*. Edited by H. Seifert. Moscow, 1964. (Translated from English.)

Kosmodem’ianskii, A. A.

*Mekhanika tel peremennoi massy (Teoriia reaktivnogo dvizheniia*), part 1. Moscow, 1947.

Fertregt, M.

*Osnovy kosmonavtiki*. Moscow, 1969. (Translated from English.)

Tsiolkovskii, K.

*E.Reaktivnye letatel’nye apparaty*. Moscow, 1964.

A. A. KOSMODEM’IANSKII