orbital mechanics

This study addresses the current absence of a standardized three-dimensional geospatial data framework capable of supporting sustainable space activities and the enforcement of international regulations, particularly in representing physical objects and their associated logical spaces—such as heritage protection zones—on extraterrestrial surfaces. To bridge this gap, the work proposes the first extraterrestrial 3D conceptual model tailored for the Moon and Mars, innovatively extending the CityJSON standard to enable unified modeling of both physical entities and logical spatial constructs. The project further develops a standardized 3D CityJSON dataset encompassing lunar landing sites and representative Martian regions, demonstrating the approach’s feasibility and potential to underpin planetary spatial data infrastructures, ensure compliance with international space law, and support the preservation of off-Earth heritage.

This work addresses the critical influence of configuration space selection on constraint satisfaction accuracy in numerical simulations of fully constrained rigid body dynamics. From a geometric perspective, the study proposes a differential-algebraic equation (DAE) formulation and geometric integration scheme based on the Lie group SE(3). It demonstrates that when kinematic constraints correspond to subgroups of SE(3), these constraints can be preserved exactly over time. The approach elucidates the intrinsic relationship between SE(3) subgroup structures and lower-pair joints, establishing that employing SE(3) as the configuration space enables strict enforcement of constraints. This result provides both a theoretical foundation and numerical guarantees for high-fidelity simulation of rigid multibody systems.

To address the challenges of maneuver prediction and collision risk assessment for rapidly deploying low-Earth-orbit (LEO) satellite constellations (e.g., Starlink), existing studies are hindered by the lack of publicly available, realistic, and temporally complete orbital datasets. This work introduces the first open-source, time-series dataset specifically designed for satellite orbit analysis. It systematically integrates Two-Line Elements (TLEs) with high-precision ephemerides (e.g., JPL DE series), followed by propagation via SGP4/SDP4, temporal alignment, and multi-source calibration to accurately characterize representative orbital maneuvers. The dataset fills a critical gap in publicly accessible data for modeling real-world LEO satellite maneuvers and supports rigorous evaluation of diverse detection algorithms. In collision warning tasks, it improves early identification accuracy by 12.7% compared to baseline approaches.

This work addresses redundancy and poor numerical stability in conventional modeling of pose, spatial velocity (twist), and generalized forces (wrench) in rigid-body kinematics. We propose a unified geometric representation framework based on dual quaternions. Methodologically, we systematically establish complete algebraic correspondences among pose transformations, differential twist motions, and wrench mappings, integrating dual-number algebra, quaternion theory, and the se(3) Lie algebra structure. Our key contribution is the first pedagogically oriented, coherent mapping framework unifying these three fundamental kinematic elements—revealing intrinsic advantages over homogeneous matrices in algebraic conciseness, differential consistency, and computational compactness. The approach significantly simplifies formula derivation in dynamics modeling and real-time control, reduces computational redundancy, and enables direct integration into robotic motion planning and control algorithms.

Nonlinear dynamics modeling and real-time control remain challenging in spacecraft orbital control, particularly across diverse orbital regimes. Method: This paper proposes a deep learning–based Koopman operator learning framework that achieves unified, data-driven global linearization for both the two-body problem (including circular, elliptical, and perturbed orbits) and the circular restricted three-body problem (CR3BP), including motion near the L1 libration point. A custom deep neural network jointly learns an optimal state-space embedding and the associated Koopman operator, yielding an equivalent linear time-invariant (LTI) system. Contribution/Results: To our knowledge, this is the first work achieving unified Koopman linearization across multiple orbital dynamical systems. Crucially, the learned Koopman operator exhibits cross-system generalizability—no retraining is required for new orbital configurations. Experiments demonstrate high-fidelity linear approximation even on unseen orbital variants, significantly enhancing modeling efficiency and enabling practical model-based control design for complex orbital dynamics.

This study addresses the limitations of existing open-source tools for planetary position and solar/lunar event computations, which often suffer from heavy dependencies, insufficient accuracy, or lack of lightweight design. To overcome these issues, this work proposes a lightweight, pure-Python astronomical computation library with no external dependencies. Built upon analytical orbital models and coordinate transformation algorithms, the library supports geocentric and heliocentric coordinate calculations, sunrise/sunset and moonrise/moonset times, lunar phases, and conversions among common astronomical coordinate systems, with optional precession corrections for compatibility across reference frames. Validation against JPL DE440 ephemerides shows mean errors of approximately 0.44′ in planetary longitude and 0.16′ in latitude, timing errors of only a few minutes for solar and lunar events, and a lunar illumination error of about 0.2%, demonstrating a favorable balance between high precision and computational efficiency.

This work addresses the simulation inconsistencies in Basilisk arising from heterogeneous development environments due to variations in dependencies, operating systems, and configurations. To resolve this, the authors propose and implement the first containerized workflow specifically designed for Basilisk. By leveraging Docker, the approach encapsulates the complete build environment, dependencies, and simulation infrastructure into a portable, self-contained package. Integrated with Basilisk’s BSKSim class hierarchy, modular dynamics modeling, and flight software integration, this framework enables reproducible end-to-end simulations—from orbital dynamics to complex Monte Carlo attitude control scenarios. The resulting environment significantly enhances the repeatability of multi-layered simulations and provides researchers with a standardized, ready-to-use Basilisk simulation platform.

The kinematics of particles and rigid bodies in the plane are investigated up to higher-order accelerations. Discussion of point trajectories leads from higher-order poles to higher-order Bresse circles of the moving plane. Symplectic geometry in vector space R^2 is used here as a new approach and leads to some new recursive vector formulas. This article is dedicated to the memory of Professor Pennestri.

Traditional approaches struggle to efficiently process the large-scale, high-dimensional orbital data of Saturn’s satellite system, hindering a deeper understanding of orbital stability and resonance structures. This work proposes a machine learning–based clustering framework that, for the first time, integrates advanced time-series feature extraction methods such as MiniRocket into astronomical orbital data analysis. By combining automated feature extraction with dimensionality reduction techniques (UMAP/t-SNE) and clustering algorithms (HDBSCAN/K-means), the method effectively characterizes approximately 22,300 simulated orbits. The approach successfully uncovers stable regions and resonant configurations within the system, offering an interpretable and scalable new paradigm for investigating the long-term dynamical evolution of Saturn’s satellites.

This work addresses the challenge of coordinate-free inverse flight dynamics modeling for fixed-wing aircraft, particularly the difficult mapping from trajectory to control inputs in tethered flight. The authors propose a novel coordinate-independent inverse dynamics framework formulated on the SO(3) manifold, which places force equilibrium in the world frame and angular momentum equations in the body frame, while geometrically defining aerodynamic force directions. Under the no-sideslip constraint, they derive a closed-form mapping from trajectory to attitude, angular velocity, and thrust–angle-of-attack pairs. By innovatively integrating geometric robotics with aerospace inverse simulation, the study reveals—for the first time—the precise balance mechanism between tether tension and centrifugal force under a zero-roll special solution, thereby decoupling aerodynamic coordination from apparent gravity. Key results include analytical expressions for roll angle in spherical parallel-circle flight and a closed-form solution for minimum-thrust angle of attack, establishing a rigorous theoretical foundation for steady-state trim and trajectory feasibility.