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CEAS EuroGNC 2026 |
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Parallel Transport of a Velocity Frame for Point Mass 3-DOF Lifting Vehicle Modeling |
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| Abstract: This paper proposes a new formulation for modeling 3-DOF lifting vehicles in Cartesian coordinates. We address the problem of describing the lift force as orthogonal to velocity vector of the vehicle, which is not well-defined in traditional models. In spherical coordinates there is a singularity in vertical flight whereas in Cartesian coordinates, using a reference direction to define the lift vector also introduces a singularity. The proposed approach consists of a moving frame carried along the trajectory by parallel transport, with its first axis remaining co-linear to the velocity vector. The other two vectors are orthogonal to the velocity vector at all time and are used to express the lift force in a well-defined manner. The advantages of this approach are illustrated in the simulation of a simplified vehicle performing a looping. | ||||
| Keywords: Parallel Transport Frame; Singularities; 3-DOF Models | ||||
 View PDF CEAS-GNC-2026-001 doi: 10.82124/CEAS-GNC-2026-001 |
| Florian Dietrich, Ioannis Sarras: Parallel Transport of a Velocity Frame for Point Mass 3-DOF Lifting Vehicle Modeling. Proceedings of the 2026 CEAS EuroGNC conference. Madrid, Spain. May 2026. doi: 10.82124/CEAS-GNC-2026-001. |
| BibTeX entry (UTF-8): @Incollection{CEAS-GNC-2026-001, author = {Dietrich, Florian and Sarras, Ioannis}, title = {Parallel Transport of a Velocity Frame for Point Mass 3-DOF Lifting Vehicle Modeling}, booktitle = {Proceedings of the 2026 {CEAS EuroGNC} conference}, address = {Madrid, Spain}, month = may, year = {2026}, doi = {10.82124/CEAS-GNC-2026-001} } |