Version 1
: Received: 27 February 2022 / Approved: 28 February 2022 / Online: 28 February 2022 (12:22:36 CET)
How to cite:
Cole, D.; Sands, T. Effect of Kinematic Algorithm Selection on the Conceptual De-Sign of Orbitally Delivered Vehicles. Preprints2022, 2022020360. https://doi.org/10.20944/preprints202202.0360.v1
Cole, D.; Sands, T. Effect of Kinematic Algorithm Selection on the Conceptual De-Sign of Orbitally Delivered Vehicles. Preprints 2022, 2022020360. https://doi.org/10.20944/preprints202202.0360.v1
Cole, D.; Sands, T. Effect of Kinematic Algorithm Selection on the Conceptual De-Sign of Orbitally Delivered Vehicles. Preprints2022, 2022020360. https://doi.org/10.20944/preprints202202.0360.v1
APA Style
Cole, D., & Sands, T. (2022). Effect of Kinematic Algorithm Selection on the Conceptual De-Sign of Orbitally Delivered Vehicles. Preprints. https://doi.org/10.20944/preprints202202.0360.v1
Chicago/Turabian Style
Cole, D. and Timothy Sands. 2022 "Effect of Kinematic Algorithm Selection on the Conceptual De-Sign of Orbitally Delivered Vehicles" Preprints. https://doi.org/10.20944/preprints202202.0360.v1
Abstract
A particular challenge in the conceptual design of direct-from orbit delivery systems is the seemingly well-known kinematics retain fallacies whose efficacies are reduced over great distances. 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. 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. One of two ubiquitous sequences of three rotations used to construct the DCM involves first a rotation around the inertial z-axis, then intermediate y-axis, then finally about the body’s x-axis; a sequence commonly called the “aerospace sequence” or the a “3-2-1 rotation sequence”. The second ubiquitous sequence is the so-called “orbital sequence” or “3-1-3 rotation sequence” with rotations about the inertial z axis first, then about the intermediate x-axis, then finally about the body z-axis. 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. Six degrees of freedom of vehicle motion were simulated starting in orbit with a given thrust and commanded maneuver. The simulation performs all twelve possible rotation sequences (transforming inertial coordinates to body coordinates) with comparison by computational burden and error representing rotations about body axes (roll, pitch, and yaw respectively). Simulation precision is validated using the quaternion normalization condition indicating near machine precision (0.9\times{10}^{-15}) and 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 so-called 321 rotation and a 99.84% increase over the so-called 313 rotation.
Keywords
GNC system design; design and analysis of orbit/attitude determination and control systems; motion planning; guidance; control; trajectory planning; conceptual design; kinematics; direction cosine matrix; DCM; 6 Degrees of Freedom; 6 DOF
Subject
Engineering, Mechanical 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.
