Chapter 1 - Reference frames and time

Abstract

This chapter discusses the reference frames commonly used in space-vehicle dynamics. A quantitative description of the motion of space vehicles—be they launch vehicles, upper stage vehicles, artificial satellites, or deep-space probes—requires one or several reference frames with respect to which the vehicle's position, velocity, and acceleration as functions of time are defined. Reference frames are also needed to describe the vehicle's attitude relative, for instance, to points on the earth, to the sun, or to guide stars. Similarly, the time derivatives of the vehicle's attitude, particularly angular rates and angular accelerations, are often needed. Implied in the use of reference frames is also the existence of a precisely defined, “uniformly” evolving time. This chapter introduces Euler angles to characterize the rotation of reference frames. Because of the importance of relative motion in such problems as fluid sloshing in the vehicle's propellant tanks or the effect of vehicle motion on gyroscopes, the transformation equations for velocities and accelerations are rederived. The need to consider two or more reference flames that are in relative motion to each other arises frequently in all branches of dynamics and is important in space technology as well. The chapter discusses the various time measurement systems that are in use in the design of space missions.