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Quasi-integrals of even-dimensional linear differential systems with skew-symmetric coefficient matrices

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Abstract

For a linear nonstationary system with skew-symmetric continuously differentiable coefficient matrix of arbitrary even dimension, we construct its quasi-integrals and obtain effective coefficient estimates for their deviations from the corresponding integrals in the stationary case. For each trajectory of motion described by such a system and lying on the sphere of the corresponding radius, these estimates permit precisely indicating a domain on the sphere containing the trajectory on a nonsmall time interval. The estimates can also be used for expanding the multidimensional motion of a mechanical object into multicomponent elements of lower dimension.

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Authors and Affiliations

  1. Institute for Mathematics, National Academy of Sciences, Minsk, Belarus

    N. A. Izobov, S. E. Karpovich, L. G. Krasnevskii & A. V. Lipnitskii

  2. Belarus State University of Computer Science and Radio Electronics, Minsk, Belarus

    N. A. Izobov, S. E. Karpovich, L. G. Krasnevskii & A. V. Lipnitskii

  3. Joint Institute of Mechanical Engineering, National Academy of Sciences, Minsk, Belarus

    N. A. Izobov, S. E. Karpovich, L. G. Krasnevskii & A. V. Lipnitskii

Authors
  1. N. A. Izobov
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  2. S. E. Karpovich
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  3. L. G. Krasnevskii
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  4. A. V. Lipnitskii
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Additional information

Original Russian Text © N.A. Izobov, S.E. Karpovich, L.G. Krasnevskii, A.V. Lipnitskii, 2008, published in Differentsial’nye Uravneniya, 2008, Vol. 44, No. 12, pp. 1595–1608.

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Izobov, N.A., Karpovich, S.E., Krasnevskii, L.G. et al. Quasi-integrals of even-dimensional linear differential systems with skew-symmetric coefficient matrices. Diff Equat 44, 1659–1672 (2008). https://doi.org/10.1134/S0012266108120021

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  • DOI: https://doi.org/10.1134/S0012266108120021

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