Location and Orientation

Abstract

The position of a body with respect to any reference frame {O ¹,e¹} is known if the locations of all the points of the body are known. Any frame having a known, possibly variable, position in space can be used as such a reference. If the body is rigid, the description of its position is very simple. A frame {O ², e²} can be embedded rigidly in the body. In this frame all points of the body have constant and known coordinates whatever the position of the body. Hence the location of all the points of a rigid body with respect to the reference frame can be determined when the position of the body-fixed frame {O ², e²} is known with respect to the reference frame {O ¹, e¹}. This relative position can be considered to be composed of the location of O ² with respect to O ¹ and of the orientation of e² with respect to e¹. Motions of the rigid body are described by parameters characterizing the relative location and orientation of the two frames as a function of time. Motion during which the relative orientation of the triads e² and e¹ does not change is called translation. When O ² remains in a fixed location with respect to O ¹ the motion is called rotation. The most general motion of a rigid body can be composed of these two simple motions.