Frames of Reference

Abstract

The solution to a mechanical problem begins with the kinematic analysis, the analysis of how a system can move, as opposed to how it actually does move under the influence of a particular set of forces. In this first stage, the essential step is the introduction of coordinates to label the configurations of the system. These might be Cartesian coordinates for the position of a particle, or angular coordinates for the orientation of a rigid body, or some complicated combination of distances and angles. The only conditions are that each physically possible configuration should correspond to a particular set of values of the coordinates; and that, conversely, the coordinates should be independent, which can be understood informally to mean that each set of values of the coordinates should determine a unique configuration. The number of coordinates is called the number of degrees of freedom of the system.