590 
Pe, y, 2) — i.e. a point with the coordinates «, y, z, relative to Ti, — 
is called the absolute velocity of P, the one relative to Ti the rela- 
tive velocity of P, the absolute velocity of a point coinciding with 
P and fixed to 7 the convection-velocity of P; they are resp. 
represented by va, Vr, Um- 
Then 
dx dy dz 
Orr == 4 Vey SH Ts Ure S TF 
‘ dien dt 2 dt 
dx \ 
Var = Una = Ure =S 5 ige hij di | 
dy 
Day = Vmy + Uy = N+ re — pz + he > oka) 
dz | 
Var = Omz — Uy z == 5 + PY — qe ss at 
where En, ¢, p,q,” have the known significations of components of 
the absolute velocity of the point O and components of the rotation 
axis when we suppose these two to be dissolved along 1X, OY, OZ. 
If Pis fixed to 7, we have 
da 
a sf ==) 
var ing Edge =rgin oo) Je 
In the following we shall as a rule indicate the absolute velocity 
of a point fixed to 7), by Um: 
If J, is the absolute acceleration of P(«, y, 2), we can express 
Jaz, Jay, Jaz in the following way. 
We choose an arbitrary fixed point P, (a,, y,, %,) i.e. fixed to Zy, 
and consider the segment ?, P, which is equal and parallel to and 
equally directed with the vector vq representing the absolute velocity 
of P; then according to its definition the absolute acceleration of P 
is equal in amount and direction to the absolute velocity of P,, 
AS &, + Var Vo + Yay: Zo + Vaz are the coordinates of P,: 
d 
Jax =§ + q (z, + Va) f (y, =F Va,y) an ze si Va,x) 3 
but the absolute velocity of the fixed point P, is equal to zero, hence 
dz, 
EH qz, 14 PN, 
so that 
