Classification in Mechanics

  1. One should not point at a deer and call it a horse. Physicists tend to classify anything that does not belong to classical mechanics as quantum mechanical in order to make it look or sound valuable (e.g. [Ashc, p.134, l.- 13, a fundamental theorem of quantum mechanics]). However, this kind of classification does not contain much meaning for engineers or other types of scientists. To make the classification meaningful, we must make it objective and specific.
        Although the origin of Bloch's theorem is related to quantum mechanics [Ashc, p.132, l.8; p.134, l.10 & l.16], the theorem quoted in [Ashc, p.134, l.- 12] should have been classified as linear algebra [Jaco, vol.2, p.134, Theorem] instead of quantum mechanics.

  2. Just like fixing a point in a plane using two coordinate axes, we use the following two bases to identify a crystal point group [Ashc, pp.121-122, Table 7.2 &Table 7.3]:
    1. Deformation hierarchy [Ashc, p.120, Fig. 7.7]: Lose symmetry by increasing deformation (i.e., changing the side length and skewing the angles).
    2. The Schoenflies or international classification: Increasing the symmetry by adding rotations, reflections, and the inversions into the group.
    Remark: We add shading to indicate what symmetries are present.

  3. Sometimes the boundary between two categories is not distinct. We can find examples which describe the continuity from one category to another [Ashc, p.388, Fig. 19.10].

  4. The classification of the Maxwell equations based on their application.
        When discussing the Maxwell equations, we refer to a special set of the Maxwell equations according to the circumstances of the application. Because each set has special features that make it slightly different than the other sets, we must be familiar with their nuances.
    1. The set for microscopic sources or vacuums: [Chou, p.19, (1.16)].
    2. The set used for macroscopic media: [Chou, p.21, (1.18)].
    3. The set in integral form: [Chou, p.23, (1.27) & (1.28); p.24, (1.29) & (1.30)].
    4. The set used for the static case (time-independent): all charges either stay in fix positions or move in a steady flow.
      1. Electrostatics: [Chou, p.30, (1.48a,b)].
      2. Magnetostatics: [Chou, p.30, (1.49a,b)].