In this paper we consider the construction and the solution of mathematical model of the spacecraft control with the help of a set of jet engines, as well as the working out the software product, which will carry out necessary calculations in accordance with the initial data and visualize the process.
This work can be divided into several stages. The first one is to consider the influence of the engine on the kinematic characteristics of these spacecraft. That is exactly how the motor runs depending on their settings, such as location, direction and how power thrust will affect the movement and rotation of the spacecraft. On the other hand, what force and moment will create a running engine?
The purpose of the second stage is to make a mathematical model that describes the behavior of a spacecraft in a certain period of time. That is, compile by the laws of the displacement and rotation of the body depending on the operating engine.
In the third stage we consider the problem of constructing an optimal trajectory of the spacecraft as a function of available resources, and the initial and final flight data. That is what engines, when and how much to work out, how would the spacecraft change its initial position, orientation in space and the speed of movement and rotation in their final results. And we will need to find an optimal solution for three cases:
1) the most rapid attainment of final parameters;
2) the lowest fuel consumption;
3) the lowest fuel consumption at the earliest possible achievement of final parameters.
The fourth and last stage consists in designing and creating software which will be implemented, building model, and also rendering the flight of the vehicle and its engine. That is when you make the initial data on the spacecraft and initial and final parameters of the system, the software should make a plan to enable or disable certain engines that have a spacecraft, depending on the model chosen to optimize the flight and come from the initial to the final state in some way.