......The other image-points
P' on the shaft shown in pictures 2
and 3 can be analytically obtained. If
a = vt (picture 3a) is the distance
covered by the observer in time t (a = vt will represent ¾on
the referent we consider for the picture¾
the movement of the shaft in time t). The points which deserve to be
studied are represented in picture 3b,
together with its Cartesian co-ordinates and supposing point O its the
origin of the system under consideration.
......With the help of picture
3a and 3b, and using the "point distance" property, we can
write:
......This is the hyperbola
equation with a/b = v/c. The shaft properties manifest themselves to the
observer is if it were at the position shown in picture 5 and twisted,
assuming the hyperbolic shape (virtual location of the shaft for the
observer, consider on time t).
Picture
4: Apparent shifting and deformation of a shaft
as the observer moves around.
......A likely study
referring to a spherical object shows that its image is shaped as an ovoid
(picture 5).
Picture
5: Apparent shifting and deformation of a
sphere as the observer moves around.
