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Generalized Euler equations in quaternions

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Abstract

The quaternion analog of the Euler dynamic equations obtained in [1–3] is generalized to the case of an arbitrary trihedron connected with a body.

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References

  1. 1.

    V.N. Koshlyakov, “Equations of motion of a heavy solid body about a fixed point,”Ukr. Mat. Zh.,25, No. 5, 677–691 (1973).

  2. 2.

    V. N. Koshlyakov, “Equations of a heavy solid body rotating around a fixed point in Rodrigues-Hamilton parameters,”Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4, 16–25 (1983).

  3. 3.

    V. N. Koshlyakov,Problems in the Dynamics of Solid Body and Applied Gyroscope Theory [in Russian], Nauka, Moscow (1985).

  4. 4.

    V. N. Branets and I. P. Shmyglevskii,Quaternions in the Problems of Orientation of a Solid Body [in Russian], Nauka, Moscow (1967).

  5. 5.

    B. V. Bulgakov,Oscillations [in Russian], Gostekhizdat, Moscow (1954).

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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1414–1416, October, 1994.

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Koshlyakov, V.N. Generalized Euler equations in quaternions. Ukr Math J 46, 1561–1564 (1994). https://doi.org/10.1007/BF01066102

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Keywords

  • Dynamic Equation
  • Euler Equation
  • Quaternion Analog
  • Euler Dynamic Equation
  • Generalize Euler Equation