Attitude Kinematics and Dynamics

Abstract

This chapter begins with a discussion of the kinematics of rotations, or attitude kinematics, and then moves on to attitude dynamics. The distinction between kinematics and dynamics is that kinematics covers those aspects of motion that can be analyzed without consideration of forces or torques. When forces and torques are introduced, we are in the realm of dynamics. To make this distinction clear, consider the motion of a point particle in Newtonian physics. If r denotes position, v denotes velocity, and time derivatives are indicated by a dot, then the kinematic equation of motion is simply ṙ=v{\$}{\$}{\backslash}dot {\{}{\backslash}mathbf {\{}r{\}}{\}}={\backslash}mathbf {\{}v{\}}{\$}{\$}. The dynamic equation of motion is mv̇=F{\$}{\$}m{\backslash}dot {\{}{\backslash}mathbf {\{}v{\}}{\}}={\backslash}mathbf {\{}F{\}}{\$}{\$} or ṗ=F{\$}{\$}{\backslash}dot {\{}{\backslash}mathbf {\{}p{\}}{\}}={\backslash}mathbf {\{}F{\}}{\$}{\$}, where F is the applied force and p{\thinspace}≡{\thinspace}mv is the translational momentum. Kinematics and dynamics are often subsumed under the single term dynamics by combining the kinematic and dynamic equations in the single relation mr̈=F{\$}{\$}m{\backslash}ddot {\{}{\backslash}mathbf {\{}r{\}}{\}}={\backslash}mathbf {\{}F{\}}{\$}{\$}. In fact, it is common in filtering theory to apply the term dynamics to any relation expressing time dependence.