Chapter 11 - Rigid body dynamics

Abstract

This chapter provides a basis for developing the equations of satellite attitude dynamics. The kinematics of rigid bodies is presented first. The motion of a rigid body is described by the displacement of any point of the body (the base point) plus a rotation about a unique instantaneous axis of rotation through that point. Describing the rotational component of the motion of a rigid body in three dimensions requires taking advantage of the vector nature of angular velocity and knowing how to take the time derivative of moving vectors. Analyzing the rotational dynamics requires computing the body’s angular momentum, and that in turn requires accounting for how the mass is distributed throughout the body. The mass distribution is described by the six components of the moment of inertia tensor. Writing the equations of rotational motion relative to coordinate axes embedded in the rigid body and aligned with the principal axes of inertia yields the nonlinear Euler equations of motion. The chapter describes how the three Euler angles and the yaw–pitch–roll angles are employed to specify the orientation of a body in three-dimensional space. The chapter concludes with a brief discussion of quaternions and an example of how they are used to describe how the attitude of a rigid body evolves.