Rotation about primary (X) axis
X1 = 0
Y1 = r cos a
Z1 = -r sin a
Rotate above system about secondary (Z) axis
X2 = Y1 sin b
Y2 = Y1 cos b
Z2 = Z1
Add translation along X axis
X = A(t) + X2
Y = Y2
Z = Z2
Where A = some constant
Total equation of motion for particle as function of time
(t):
For the case under consideration:
A = 1
r = .5
b = 22.5(t) degrees
a = 2b
Thus:
X = t + .5 cos(45t)sin(22.5t)
Y = .5 cos(45t)cos(22.5t)
Z = -.5 sin(45t)
