Bra-Ket Representation of the Inertia Tensor

U. Rae Kim, Dohyun Kim, Jungil Lee

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We employ Dirac’s bra-ket notation to define the inertia tensor operator that is independent of the choice of bases or coordinate system. The principal axes and the corresponding principal values for the elliptic plate are determined only based on the geometry. By making use of a general symmetric tensor operator, we develop a method of diagonalization that is convenient and intuitive in determining the eigenvector. We demonstrate that the bra-ket approach greatly simplifies the computation of the inertia tensor with an example of an N-dimensional ellipsoid. The exploitation of the bra-ket notation to compute the inertia tensor in classical mechanics should provide undergraduate students with a strong background necessary to deal with abstract quantum mechanical problems.

Original languageEnglish
Pages (from-to)945-951
Number of pages7
JournalJournal of the Korean Physical Society
Issue number11
Publication statusPublished - 2020 Dec


  • Bra-ket notation
  • Classical mechanics
  • Diagonalization
  • Hyperellipsoid
  • Inertia tensor

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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