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Baker–Campbell–Hausdorff–Dynkin Formula for the Lie Algebra of Rigid Body Displacements

Author

Listed:
  • Daniel Condurache

    (Technical University of Iasi, D. Mangeron 59, 700050 Iasi, Romania
    Technical Sciences Academy of Romania, B-dul Dacia, 26, 030167 Bucharest, Romania)

  • Ioan-Adrian Ciureanu

    (“Grigore T. Popa” University of Medicine and Pharmacy Iasi, 700116 Iasi, Romania)

Abstract

The paper proposes, for the first time, a closed form of the Baker–Campbell–Hausdorff–Dynkin (BCHD) formula in the particular case of the Lie algebra of rigid body displacements. For this purpose, the structure of the Lie group of the rigid body displacements S E ( 3 ) and the properties of its Lie algebra s e ( 3 ) are used. In addition, a new solution to this problem in dual Lie algebra of dual vectors is delivered using the isomorphism between the Lie group S E ( 3 ) and the Lie group of the orthogonal dual tensors.

Suggested Citation

  • Daniel Condurache & Ioan-Adrian Ciureanu, 2020. "Baker–Campbell–Hausdorff–Dynkin Formula for the Lie Algebra of Rigid Body Displacements," Mathematics, MDPI, vol. 8(7), pages 1-19, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1185-:d:386589
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