Stationkeeping at libration points of natural elongated bodies

Prieto-Llanos, Tomás; Gómez-Tierno, Miguel A.

doi:10.2514/3.21268

Cited by 34 publications

(10 citation statements)

References 4 publications

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“…Such a boundary is usually called the "zero-velocity surface" corresponding to the case of C = V . It has been found that when κ 0.125 the non-collinear equilibrium points no longer exist [13,18]. In this study, the feasible region of the force ratio is κ > 0.125 to guarantee that there are always two triangular equilibrium points around the dipole model.…”

Section: Uniformly Rotating Mass Dipolementioning

confidence: 77%

“…All the five equilibria are unstable according to Ref. [13]. The name of these equilibria pinpointed with E 1 to E 5 is similar to the traditional Lagrange points L 1 to L 5 of the CRTBP.…”

Section: Periodic Orbits Around the Dipole Model (I)mentioning

confidence: 90%

“…According to previous studies [13,18], there are totally three topological cases for the dipole model. The first case was discussed in Section 3 with five unstable equilibrium points.…”

Section: Periodic Orbits Around the Dipole Model (Ii)mentioning

confidence: 99%

“…It was then applied to the binary system, such as the Mars-Phobos system [13] and also to approximate a symmetrical rotating dumbbell [14]. In this study periodic orbits around the dipole model will be generated and analyzed.…”

Section: Introductionmentioning

confidence: 99%

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Periodic orbits in the Chermnykh problem

Zeng

Alfriend

2017

Astrodyn

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Periodic orbits in irregular gravitational fields are significant for an understanding of dynamical behaviors around asteroids as well as the engineering aspect for deep space explorations. The rotating mass dipole, referred to as the Chermnykh problem, is a good alternative model to study qualitative dynamical environments near elongated asteroids, like the asteroid 1620 Geographos, 216 Kleopatra, or 25143 Itokawa. In this paper a global searching method is adopted to search for periodic orbits around the dipole model

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Section: Uniformly Rotating Mass Dipolementioning

confidence: 77%

“…All the five equilibria are unstable according to Ref. [13]. The name of these equilibria pinpointed with E 1 to E 5 is similar to the traditional Lagrange points L 1 to L 5 of the CRTBP.…”

Section: Periodic Orbits Around the Dipole Model (I)mentioning

confidence: 90%

“…According to previous studies [13,18], there are totally three topological cases for the dipole model. The first case was discussed in Section 3 with five unstable equilibrium points.…”

Section: Periodic Orbits Around the Dipole Model (Ii)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Periodic orbits in the Chermnykh problem

Zeng

Alfriend

2017

Astrodyn

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“…Position and velocity sensitivity studies were performed and concluded that while injection positions show little change over long-term projections, injection velocities must be tightly controlled. Prieto-Llanos and Gómez-Tierno [6] have simulated stationkeeping scenarios about the L1 libration point of Phobos using a discrete-time modal controller. Although the controller is robust in the presence of model errors in mass, the L1 point of Phobos is naturally unstable and allows limited observation of the moon.…”

Section: Introductionmentioning

confidence: 99%

Control strategies for stable orbits around phobos

Takacs¹,

Damaren²

Proceedings of 2005 IEEE Conference on Control Applications, 2005. CCA 2005.

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This study compares three linear optimal controllers for stationkeeping with respect to reference orbits around Phobos. The dynamics of the Mars-Phobos system are constrained to the synodical plane of the circular restricted three-body problem (CRTBP) with Phobos modelled as an ellipsoid. The controllers rely on periodic orbits which permit the dynamics to be expressed as a linear system with periodic coefficients. A novel method of determining the necessary conditions for periodic orbits is formulated through nonlinear optimization techniques, where the function to be minimized is the vector norm of the difference between the initial and final conditions of the orbit. The optimization algorithm is a Nelder-Mead simplex and is shown to outperform any gradientbased methods as well as other techniques for determining such orbits. Two controllers, constant feedback and scheduled, are developed from the algebraic Riccati equation (ARE), which is solved at specific points on the reference orbits. These controllers are then compared to the optimal solution which uses the time-varying Riccati equation. At high orbits, the periodicity of the linearized system is very small and the controllers are nearly identical in performance. Closer orbits reveal increases in the periodicity of the dynamics, leading to an increase in performance of the time-varying Riccati equationbased controller over the scheduled and constant feedback gain cases.

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