GEOMETRY OF MOTION. 



[45- 



V. Composition and Resolution of Displacements. 

 i. TRANSLATIONS; VECTORS. 



45. All the points of a rigid body subjected to a translation 

 describe parallel and equal lines (Art. 9). The translation of 

 the body is therefore fully determined by the displacement A^A^ 



of any one point A of the 

 body (Fig. 12), and can be 

 represented geometrically by 

 A Q A 1 or any line equal and 

 parallel to it, like 01. 



A segment of a straight 

 line of definite length, direc- 

 tion, and sense is called a 



C, 



Fig. 12. 



vector. The sense of the 

 vector (see Art. 6) which 

 expresses whether the translation is to take place from o to i or 

 from i to o, is indicated graphically by an arrow-head, and in 

 naming the vector, by the order of the letters, 01 and 10 being 

 vectors of opposite sense. 



46. Imagine a rigid body subjected to two successive trans- 

 lations. From any point o (Fig. 13) draw a vector 01 

 representing the first translation, and from its end I a vector 

 12 representing the second transla- 

 tion. The vector 02 will then repre- 

 sent a translation that would bring 

 the body directly from its initial to 

 its final position. This vector 02 is 

 called the geometric sum, or the resul- 

 tant, of the vectors 01 and 12, which 

 are called the components. The oper- 

 ation of combining the components into a resultant, or of 

 finding the geometric sum of two vectors, is called geometric 

 addition, or composition, of vectors. 



Fig. 13. 



