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A Full-Body Relative Orbital Motion of Spacecraft Using Dual Tensor Algebra and Dual Quaternions

Author

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  • Daniel Condurache

    (Department of Theoretical Mechanics, Technical University of Iasi, D. Mangeron Street No.59, 700050 Iasi, Romania)

Abstract

This paper proposes a new non-linear differential equation for the six degrees of freedom (6-DOF) relative rigid bodies motion. A representation theorem is provided for the 6-DOF differential equation of motion in the arbitrary non-inertial reference frame. The problem of the 6-DOF relative motion of two spacecraft in the specific case of Keplerian confocal orbits is proposed. The result is an analytical method without secular terms and singularities. Tensors dual algebra and dual quaternions play a fundamental role, with the solution representation being the relative problem. Furthermore, the representation theorems for the rotation and translation parts of the 6-DOF relative orbital motion problems are obtained.

Suggested Citation

  • Daniel Condurache, 2023. "A Full-Body Relative Orbital Motion of Spacecraft Using Dual Tensor Algebra and Dual Quaternions," Mathematics, MDPI, vol. 11(6), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1366-:d:1094322
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    References listed on IDEAS

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    1. Oleksandr Tsymbal & Paolo Mercorelli & Oleg Sergiyenko, 2021. "Predicate-Based Model of Problem-Solving for Robotic Actions Planning," Mathematics, MDPI, vol. 9(23), pages 1-13, November.
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