Lagrange–Poincaré–Kepler equations of disturbed space-manipulator systems in orbit
Bibliographic record
Abstract
This article presents an extension of the Lagrange-Poincaré Equations (LPE) to model the dynamics of spacecraft-manipulator systems operating within a non-inertial orbital reference frame. Building upon prior formulations of LPE for vehicle-manipulator systems, the proposed framework—termed the Lagrange-Poincaré-Kepler Equations (LPKE)—incorporates the coupling between spacecraft attitude dynamics, orbital motion, and manipulator kinematics. The formalism combines the Euler-Poincaré equations for the base spacecraft, Keplerian orbital dynamics for the reference frame, and reduced Euler–Lagrange equations for the manipulator’s shape space. Using the Lagrange-d’Alembert principle, we derive closed-form structural matrices that explicitly capture the effects of orbital disturbances and their dynamic coupling with the manipulator. The framework naturally includes symmetry-breaking wrenches and integrates into hardware-in-the-loop simulations and model-based control architectures. A simulation study of a 7-DOF orbital manipulator demonstrates the effectiveness and numerical advantages of the LPKE formulation. • Developing Lagrangian equations for perturbed space manipulators in orbit. • Decoupling rigid and internal motion of space manipulators in an orbital frame. • Including arbitrary forcing functions in the equations. • Demonstrating numerical superiority comparing to classical methods.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".