Rosalin Pradhan,
Sidhartha Kumar Samal,
Bibhu Prasad Ganthia,
- Assistant Professor, Department of Electrical Engineering, Indira Gandhi Institute of Technology, Sarang, Dhenkanal, Odisha, India
- Assistant Professor, Department of Electrical Engineering, Indira Gandhi Institute of Technology, Sarang, Dhenkanal, Odisha, India
- Assistant Professor, Department of Electrical Engineering, Indira Gandhi Institute of Technology, Sarang, Dhenkanal, Odisha, India
Abstract
Autonomous spacecraft operating in Earth orbit are subjected to coupled translational and rotational dynamics influenced by gravitational and environmental perturbations. Accurate mathematical characterization of these interactions is essential for trajectory prediction, attitude stabilization, autonomous navigation, and mission reliability. This study develops a nonlinear mathematical framework for coupled orbital–attitude dynamics of an autonomous spacecraft under perturbative forces. The translational dynamics are formulated using the two-body gravitational model augmented by the second zonal harmonic, atmospheric drag, and solar-radiation pressure. The rotational dynamics are derived using Euler’s rigid-body equations and quaternion-based attitude kinematics to avoid singularities associated with classical attitude parameterizations. The perturbative forces are transformed into the spacecraft body frame to establish explicit coupling between orbital and attitude states. The complete system is subsequently expressed in nonlinear state-space form, and an equilibrium operating condition is derived for local stability analysis. Linearization around the equilibrium produces a Jacobian matrix whose eigenvalues characterize the dynamic modes of the coupled system. A Lyapunov-based stability formulation is additionally developed to establish a sufficient condition for local asymptotic stability. The formulation also permits sensitivity analysis with respect to spacecraft mass, inertia, orbital altitude, atmospheric density, solar-radiation pressure, and gravitational perturbation coefficients. The resulting framework provides a mathematically transparent approach for assessing perturbation-induced orbital deviations and attitude responses and can support the design and analysis of autonomous spacecraft guidance, navigation, and control systems.
Keywords: Autonomous Spacecraft; Orbital Dynamics; Attitude Dynamics; Perturbative Forces; Gravitational Perturbation
[This article belongs to Research & Reviews : Journal of Space Science & Technology ]
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Research & Reviews : Journal of Space Science & Technology
| Volume | 15 | |
| Issue | 02 | |
| Received | 22/09/2026 | |
| Accepted | 24/09/2026 | |
| Published | 24/09/2026 | |
| Publication Time | 2 Days |