Rocket Dynamics
Summary
This virtual laboratory is concerned with the dynamics of rockets.
A simple model of a rocket will be used to learn how stability depends upon design parameters. We also learn about linearisation of nonlinear dynamical equations and the role of the operating point in determining the local dynamics of a nonlinear system.
This Laboratory was designed and contributed by Jim Kusters (A Masters student from the Technical University of Eindhoven, Netherlands. The laboratory was written while he was a visiting postgraduate student at the University of Newcastle, Australia) with advice from Professor Robert Skelton (From University of California, San Diego’s Department of Mechanical and Aerospace Engineering. Professor Skelton was a visiting academic at the University of Newcastle and was able to give advice to Jim Kusters during the preparation of this laboratory).
Figure 10.1: Screenshot of Program
The Physical Apparatus
This virtual laboratory is about the dynamics of rockets similar to the one shown in figure 10.2. This particular picture shows a Redstone rocket and its appearance is typical of rockets used by agencies such as NASA, the European Space Agency and an increasing number of other organisations, to launch satellites, exploration vehicles and to service orbiting stations. Modern rocketry has its roots in the German V1 and V2 rocket programme during the second world war. After the war, the scientists responsible for this work found their way, either to the USA or Soviet Russia. In 1957 Soviet rocket scientists astounded the world with the launch via a rocket, of the world’s first artificial satellite Sputnik 1. This achievement astounded the world, and was the stimulus for an intense research and development exercise in rocketry in the USA. Ambitious targets were announced to equal and surpass the Russian achievements, and the Space Race began (see Tom Wolfe’s book ‘The Right Stuff’ (Bantam Press, 1980) for a readable account of this period). Consult also Wikipedia.
Time has moved on, and the use of rockets is now almost routine indeed essential in a world in which communications is controlled by orbiting telecommunications satellites. Despite the almost routine nature of rocketry, rocket launch vehicles are spectacular examples of aerospace engineering in which control engineering plays a crucial role. In particular, the stability of a rocket is dependent upon properly designed control systems which regulate the angle at which thrust is applied to the rocket body. With the rocket itself, the fins at the base of the body (clearly visible in figure 10.1) give some stability. However, it is stabilising feedback control that keeps the rocket from tumbling out of control.
In this, the first of two virtual laboratories, we will use a simple model of a rocket like the Redstone and learn how its stability depends upon design parameters. Along the way you will learn about linearisation of nonlinear dynamical equations and the role of operating point in determining the local dynamics of a nonlinear system. Starting with a statement of the nonlinear equations of motion for a rocket flying in the x, y plane, we explain the concepts of linearisation about an operating point. Linearised models of the rocket dynamics are then used to understand rocket dynamics including the tumbling phenomenon.
Figure 10.2: A Redstone Rocket at Take Off (original image by NASA copyright freesource Wikipedia)
Prerequisites
We assume that you have:
- a knowledge of root locus methods
- an understanding of state space models of transfer function models
Learning Objectives
The objectives of this laboratory are:
- To introduce the student to the dynamics of a simplified rocket in flight.
- To introduce the student to the dynamics of a simplified rocket in flight.
- To show how rocket design influences its stability in flight.
- To learn about linearisation of nonlinear dynamical equations.
- To use Linearised equations to show how rocket parameters effect stability.
