BULETINUL INSTITUTULUI POLITEHNIC DIN IAI Publicat de Universitatea Tehnic „Gh. Asachi“, Iai, Tomul LII (LVI), Fasc. 6X, 2006 Sec ia CONSTRUCII DE MAINI COMPUTING THE FIELD OF n th ORDER ACCELERATIONS IN RIGID MOTION BY DIRECT MEASUREMENTS BY DANIEL CONDURACHE and VLADIMIR MARTINUI Abstract: By using tensorial considerations, the paper presents a systematic approach to the nth order acceleration field in rigid kinematics. The nth order acceleration tensor and the nth order acceleration invariant are computed by direct measurements. Necessary and sufficient conditions for the existence of the nth order acceleration pole are established. Key words: n th order acceleration tensor, n th order acceleration invariant Nomenclature: n I = n th order acceleration invariant “ × a b ”= the cross product of vectors a and b. n R = proper orthogonal tensor “ ⊗ a b ”= the dyadic product of vectors a and b. n  = n th order acceleration tensor “ ( ) , , abc ”= the triple scalar product of vectors a, b, c.. 3 SO  = the set of functions with the domain  (the set of real numbers) and the range the set of orthogonal proper tensors  = absolute position vector 3 so  = the set of functions with the domain  and the range the set of skew-symmetric- tensors v = absolute velocity “ ⋅ ab ”= the dot product of vectors a and b. a (n) = n th order absolute acceleration