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Solving Quaternion Ordinary Differential Equations with Two-Sided Coefficients

Solving Quaternion Ordinary Differential Equations with Two-Sided Coefficients The theory of quaternion differential equations (QDEs) has recently received a lot of attention. They have numerous applications in physics and engineering problems. In the present investigation, a new approach to solve the linear QDEs is achieved. Specifically, the solutions of QDEs with two-sided coefficients are studied via the adjoint matrix technique. That is, each quaternion can be uniquely expressed as a form of linear combinations of two complex numbers. By applying the complex adjoint representation of quaternion matrix, the connection between QDEs, with unilateral or two-sided coefficients, and a system of ordinary differential equations is achieved. By a novel specific algorithm, the solutions of QDEs with two-sided coefficients are fulfilled. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Qualitative Theory of Dynamical Systems Springer Journals

Solving Quaternion Ordinary Differential Equations with Two-Sided Coefficients

Cai, Zhen; Kou, Kit
Qualitative Theory of Dynamical Systems , Volume 17 (2) – Jul 11, 2017
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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer International Publishing AG
Subject
Mathematics; Mathematics, general; Dynamical Systems and Ergodic Theory; Difference and Functional Equations
ISSN
1575-5460
eISSN
1662-3592
DOI
10.1007/s12346-017-0246-z
Publisher site
See Article on Publisher Site

Abstract

The theory of quaternion differential equations (QDEs) has recently received a lot of attention. They have numerous applications in physics and engineering problems. In the present investigation, a new approach to solve the linear QDEs is achieved. Specifically, the solutions of QDEs with two-sided coefficients are studied via the adjoint matrix technique. That is, each quaternion can be uniquely expressed as a form of linear combinations of two complex numbers. By applying the complex adjoint representation of quaternion matrix, the connection between QDEs, with unilateral or two-sided coefficients, and a system of ordinary differential equations is achieved. By a novel specific algorithm, the solutions of QDEs with two-sided coefficients are fulfilled.

Journal

Qualitative Theory of Dynamical Systems – Springer Journals

Published: Jul 11, 2017

References

  • Quaternionic quantum field theory
    Adler, S
  • Quaternionic Quantum Mechanics and Quantum Fields
    Adler, S
  • Delay time in quaternionic quantum mechanics
    Leo, S; Ducati, G
  • Quaternionic potentials in non-relativistic quantum mechanics
    Leo, S; Ducati, G; Nishi, C
  • Spacecraft Attitude Determination and Control
    Wertz, J
  • An alternative derivation of the quaternion equations of motion for rigid-body rotational dynamics
    Udwadia, F; Schttle, A
  • A quaternionic structure in the three-dimensional euler and ideal magneto-hydrodynamics equation
    Gibbon, J
  • Quaternions and particle dynamics in the euler fluid equations
    Gibbon, J; Holm, D; Kerr, R; Roulstone, I
  • Examples of quaternionic and keller structures in hamiltonian models of nearly geostrophicow
    Rubtsov, V; Roulstone, I
  • Holomorphic structures in hydrodynamical models of nearly geostrophicow
    Rubtsov, V; Roulstone, I
  • Quaternion frame approach to streamline visualization
    Handson, A; Ma, H
  • Models of hopfield-type quaternion neural networks and their energy functions
    Yoshida, M; Kuroe, Y; Mori, T
  • Periodic solutions of quaternionic-valued ordinary differential equations
    Campos, J; Mawhin, J
  • Solving simple quaternionic differential equations
    Leo, S; Ducati, G
  • Quaternionic valued ordinary differential equations. The Riccati equation
    Wilczynski, P
  • Quaternionic-valued ordinary differential equations II: coinciding sectors
    Wilczynski, P
  • Global structure of quaternion polynomial differential equations
    Zhang, X
  • Global u-stability criteria for quaternion-valued neural networks with unbounded time-varying delays
    Liu, Y; Zhang, D; Lu, J; Cao, J
  • Optimization in quaternion dynamic systems: gradient, Hessian, and learning algorithms
    Xu, D; Xia, Y; Mandic, D
  • Quaternionic factorization of the schrodinger operator and its applications to some first order systems of mathematical physics
    Kravchenko, V; Kravchenko, V
  • Quaternions and matrices of quaternions
    Zhang, F
  • Jordan canonical form of a partitioned complex matrix and its application to real quaternion matrices
    Zhang, F; Wei, Y
  • Advanced Engineering Mathematics
    Kreyszig, E
  • A solution of two demensional linear homogeneous second order differential eguation with constant coefficients
    Huang, J
  • Matrices of quaternions
    Brenner, J
  • Zeros of two-sided quadratic quaternion polynomials
    Xu, W; Feng, L; Yao, B
  • Linear quaternionic equations and their systems
    Shpakivskyi, V
  • Extreme ranks of real matrices in solution of the quaternion matrix equation axb = c with applications
    Wang, Q; Yu, S; Xie, W