Periodic Motion of Rigid Body in Circular Orbit

AbstractThe equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and the angular velocity of the prescribed rigid-body motion are compatible, and that the mean translational velocity is non-zero, existence of a time-periodic solution is established. The proof is based on an appropriate linearization, which is examined within a setting of absolutely convergent Fourier series. Since the corresponding resolvent problem is ill-posed in classical Sobolev spaces, a linear theory is developed in a framework of homogeneous Sobolev spaces.

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The J 2 Relative Perturbation Analysis of Satellite Formation under the Requirement of Relative Position Maintenance with Millimeter-Level Accuracy

International Journal of Aerospace Engineering ◽

10.1155/2021/6687468 ◽

2021 ◽

Vol 2021 ◽

pp. 1-9

Author(s):

Jingji Wang ◽

Chunyang Liu

Keyword(s):

Relative Position ◽

Periodic Motion ◽

Circular Orbit ◽

Level Control ◽

Zonal Harmonic ◽

Target Indicator ◽

Digital Elevation ◽

Elevation Model ◽

Control Accuracy

With high-precision DEM (Digital Elevation Model) and GMTI (Ground Moving Target Indicator) as the demand background, the influence of J 2 zonal harmonic term perturbation on the relative motion of the millimeter-level short-range leader-follower satellites in near-circular orbit is studied through the relative perturbation method. An equation of motion that can describe the motion of the leader-follower satellites under the influence of J 2 perturbation in near-circular orbit is derived, and the characteristics of the trajectory of in-plane periodic motion are analyzed. A study shows that under the influence of the relative perturbation of the J 2 term, the in-plane periodic motion of the leader-follower satellites in near-circular orbit is a symmetrical closed “drop-shaped” trajectory with a period of 2 π / n . By comparing with the results of numerical simulations, the correctness of the conclusions obtained in this paper is verified. According to the research results, it can be known that only using a thruster as the actuator to maintain the relative position can no longer meet the requirements of the long-term mm-level relative position maintenance. In the future, a new technical approach needs to be explored to achieve the long-term relative position maintenance with millimeter-level control accuracy.

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