Thermal center

The thermal center is a concept used in applied mechanics and engineering.

Photolitography machines and high precision optical instruments are some examples of application of this concept.

Analyzing this phenomenon in an absolute coordinate system, the transformation of the solid body is a geometrical similarity.

It is possible that, choosing the constrains conveniently, one point belonging to the space associated to the body will not move during the thermal variation: this point is called thermal center.

Picture B shows an example where the geometry of the constraints doesn't come to a unique point.

The TC may exist even if the body has non-homogeneous isotropic thermal properties, but when this condition is not verified, it's not possible to determine its position by using the simple geometric method shown above, and the transformation will not be a homothety.

Picture of the thermal center.
Picture A: geometric construction of the thermal center: under the mentioned hypothesis, thermal center position is only function of the constraints. Picture B: This is an example of thermal center not defined, since the geometrical construction leads to different points for different expansions.