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

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 o...

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Bibliographic Details
Published inMathematics (Basel) Vol. 11; no. 6; p. 1366
Main Author Condurache, Daniel
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.03.2023
Subjects
Algebra
Attitudes
Degrees of freedom
dual algebra
Equations of motion
full body problem
Inertial reference systems
Kinematics
Lie groups
Mathematical analysis
Mathematics
Mechanical properties
non-inertial frame
Nonlinear differential equations
Orbits
Quaternions
relative orbital motion
Representations
Rigid structures
Space ships
Space vehicles
Spacecraft
Tensors
Tensors (Mathematics)
Theorems
Romania
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11061366