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تسجيل مستخدم جديدFourth-order gravity gradient torque of spacecraft orbiting asteroids
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The dynamical behavior of spacecraft around asteroids is a key element in design of such missions. An asteroids irregular shape, non-spherical mass distribution and its rotational sate make the dynamics of spacecraft quite complex. This paper focuses on the gravity gradient torque of spacecraft around non-spherical asteroids. The gravity field of the asteroid is approximated as a 2nd degree and order-gravity field with harmonic coefficients C20 and C22. By introducing the spacecrafts higher-order inertia integrals, a full fourth-order gravity gradient torque model of the spacecraft is established through the gravitational potential derivatives. Our full fourth-order model is more precise than previous fourth-order model due to the consideration of higher-order inertia integrals of the spacecraft. Some interesting conclusions about the gravity gradient torque model are reached. Then a numerical simulation is carried out to verify our model. In the numerical simulation, a special spacecraft consisted of 36 point masses connected by rigid massless rods is considered. We assume that the asteroid is in a uniform rotation around its maximum-moment principal axis, and the spacecraft is on the stationary orbit in the equatorial plane. Simulation results show that the motion of previous fourth-order model is quite different from the exact motion, while our full fourth-order model fits the exact motion very well. And our model is precise enough for practical applications.
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Purpose: This paper presents a full fourth-order model of the gravity gradient torque of spacecraft around asteroids by taking into consideration of the inertia integrals of the spacecraft up to the fourth order, which is an improvement of the previo
us fourth-order model of the gravity gradient torque. Design, methodology and approach: The fourth-order gravitational potential of the spacecraft is derived based on Taylor expansion. Then the expression of the gravity gradient torque in terms of gravitational potential derivatives is derived. By using the formulation of the gravitational potential, explicit formulations of the full fourth-order gravity gradient torque are obtained. Then a numerical simulation is carried out to verify our model. Findings: We find that our model is more sound and precise than the previous fourth-order model due to the consideration of higher-order inertia integrals of the spacecraft. Numerical simulation results show that the motion of the previous fourth-order model is quite different from the exact motion, while our full fourth-order model fits the exact motion very well. Our full fourth-order model is precise enough for high-precision attitude dynamics and control around asteroids. Practical implications: This high-precision model is of importance for the future asteroids missions for scientific explorations and near-Earth objects mitigation. Originality and value: In comparison with the previous model, a gravity gradient torque model around asteroids that is more sound and precise is established. This model is valuable for high-precision attitude dynamics and control around asteroids.
The classical problem of attitude stability in a central gravity field is generalized to that on a stationary orbit around a uniformly-rotating asteroid. This generalized problem is studied in the framework of geometric mechanics. Based on the natura
l symplectic structure, the non-canonical Hamiltonian structure of the problem is derived. The Poisson tensor, Casimir functions and equations of motion are obtained in a differential geometric method. The equilibrium of the equations of motion, i.e. the equilibrium attitude of the spacecraft, is determined from a global point of view. Nonlinear stability conditions of the equilibrium attitude are obtained with the energy-Casimir method. The nonlinear attitude stability is then investigated versus three parameters of the asteroid, including the ratio of the mean radius to the stationary orbital radius, the harmonic coefficients C20 and C22. It is found that when the spacecraft is located on the intermediate-moment principal axis of the asteroid, the nonlinear stability domain can be totally different from the classical Lagrange region on a circular orbit in a central gravity field.
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