Article
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Complex Dynamical Orbit Re-entry Navigation and Control
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Version 1
: Received: 8 December 2023 / Approved: 12 December 2023 / Online: 12 December 2023 (05:08:34 CET)
How to cite: Cole, D.; Sands, T. Complex Dynamical Orbit Re-entry Navigation and Control. Preprints 2023, 2023120787. https://doi.org/10.20944/preprints202312.0787.v1 Cole, D.; Sands, T. Complex Dynamical Orbit Re-entry Navigation and Control. Preprints 2023, 2023120787. https://doi.org/10.20944/preprints202312.0787.v1
Abstract
Calculating a minimum-time trajectory requires the solving of a boundary value problem resulting from invocation of necessary conditions of optimality to set up a set of ordinary differential equations to solve the trajectory between the initial position and desired ending position with set constraints on the path between the two. This manuscript expresses the minimum time optimum trajectory between a satellite in a geosynchronous orbit and a target set on earth’s surface utilizing a non-rotating earth centric coordinate system. Expressing motion in coordinates of rotating reference frames necessitates transformation between reference frames, and one such transformation is embodied in the Direction Cosine Matrices (DCM) formed by a sequence of three successive frame rotations. Rotation about the local wing of an aerospace vehicle is almost never the pitch angle, yet modern application of kinematics often assumes such (with accompanying angular error). The same assertion is usually true about the nature of roll and yaw angles. This manuscript evaluates which sequence is the most advantageous for an object starting in space and then travels through the atmosphere to a target on the Earth’s surface. Simulation precision (validated by the quaternion normalization condition) reveals the so-called 132 rotation is the most accurate with an average error of 0.14° and a computational time of 0.013 seconds: resulting in a 97.95% increase in accuracy over the ubiquitous 321 “aerospace” rotation sequence and a 99.84% increase over the so-called 313 “orbital” rotation sequence. Utilizing the proposed optimal trajectory candidate yields a total flight time of 2 hours, 34 minutes and 46 seconds, or an average velocity of 3.85 kilometers per second, while impacting the target with a velocity of 11.54 kilometers per second.
Keywords
convex optimization; trajectory optimization; path planning; kinematics
Subject
Engineering, Aerospace Engineering
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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