Computational Frameworks for Aerospace Vehicle Design: A Systematic Review of 3D Kinematics, Coordinate Transformation, Angular Momentum, and Inertia Tensor Analysis
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Abstract
Many mathematical models are needed in the design of modern aerospace vehicle to model the complex three dimensional motion, coordinate transformation, dynamics of angular momentum, and characteristics of the inertia tensor. This systematic review provides an overview of the methodological progress in 3D flight mechanics, coordinate transformations and rotational dynamics, and to derive synthesized 3D integrated guidance, navigation and control (GNC) design frameworks. A thorough literature review was carried out using the following databases: Scopus, IEEE Xplore, Web of Science, Google Scholar, AIAA Electronic Library and the NASA Technical Reports Server for peer-reviewed literature published from 01/2012 to 05/2026. Studies involving 6-DOF kinematics, frame transformations, angular momentum or inertia tensors in aerospace design were included. Studies published prior to 2012, non-English publications and conference abstracts were not included. The methodological quality was assessed with Joanna Briggs Institute (JBI) critical appraisal tools and then a qualitative narrative synthesis was conducted. 1,420 initial records were identified from a database search and 61 studies were included who fulfilled all inclusion criteria. The synthesis shows the fundamental transition from assuming rigid bodies to accounting for variable mass Lagrangian dynamics and dynamic inertia tensor tracking (I ̇). In the end, unit quaternions became the most popular non-singular way of representing attitude in control for agility, in place of Euler angles. Moreover, coupling full 6-DOF constraints with convex optimization and physics-informed machine learning allowed real-time generation of an onboard trajectory on GPUs and FPGAs. Combining variable-mass kinematics, quaternion transformations and adaptive estimation of the inertia tensor is a key element of the next generation of aerospace vehicles. Further work is needed to focus on hardware accelerated convex optimization, sensor driven digital twins and uncertainty quantification for autonomous operation in extreme atmospheric conditions.
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