New State Transition Matrix for Relative Motion on an Arbitrary Keplerian Orbit

Dang, Zhaohui

doi:10.2514/1.g002723

Cited by 15 publications

(9 citation statements)

References 18 publications

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“…where T 1 2 is the transformation matrix from the orbit 1 reference frame to the orbit 2 reference frame; and r 2 and r 1 are, in their own orbit reference systems, the position vectors of two spacecraft: (14) By rotating the orbit 1 reference frame through ϕ 1 along its z axis, then through θ along the x axis of the once rotated system, and finally −ϕ 2 along the z axis of the twice-rotated system, the orbit 1 reference frame will coincide with that of orbit 2. Defining T x ⋅ and T z ⋅ as the rotation matrix functions of the rotation angle along the x and z axes, respectively, the rotation matrix from orbit 1 to orbit 2 is Left multiplying r 2 and T 1 2 r 1 by T x −1∕2θT z −ϕ 2 , the observation model is then given in a symmetric formation as…”

Section: B Observation Modelmentioning

confidence: 99%

See 1 more Smart Citation

Relative Orbit Determination Using Only Intersatellite Range Measurements

Qin

Dong

Macdonald

2019

Journal of Guidance, Control, and Dynamics

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Section: B Observation Modelmentioning

confidence: 99%

“…The matrix should be mapped to the initial epoch t 0 through the state transformation matrix (STM) [14] as…”

Section: Observability Matrixmentioning

confidence: 99%

Relative Orbit Determination Using Only Intersatellite Range Measurements

Qin

Dong

Macdonald

2019

Journal of Guidance, Control, and Dynamics

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“…Wang Gongbo [14][15] deduced a space circular formation dynamics model for a circular orbit under the condition of continuous small thrust. Dang Zhaohui [16][17] derived a new state transition matrix of relative motion in any Keplerian orbit and gave the solution of the TH equation.…”

Section: Introductionmentioning

confidence: 99%

Mission Planning for Optical Satellite’s Constant Surveillance to Geostationary Spacecraft

Zhang¹,

Z²,

Wang³

et al. 2021

Preprint

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For a mission to constantly watch geostationary (Orbital inclination isn’t 0, GEO) spacecraft by an optical satellite during a whole fly-around cycle, study the relative position relationship between the two and sun during fly-around mission; design the trajectory of the optical satellite, on which, the optical satellite keeps facing to the spacecraft in the direction opposite the Sun. Firstly, for constant surveillance to geosynchronous (Orbital inclination is 0) spacecraft, study from the Keplerian orbit elements, analyze its geometric relationship with the sun and the optical satellite. Then calculate the initial phase interval that meets the requirements of the mission. Compared with Clohessy-Wiltshire equation (CW equation), this method is more concise and the spatial physical meaning is clearer. However, the orbital inclination of GEO spacecraft is usually not 0. Secondly, taking GEO spacecraft with 1° inclination as an example, calculate the initial phase interval of the mission. Thirdly, select an initial phase in the initial phase interval, and design the fly-around trajectory based on CW equation. Lastly, the optical satellite’s position when it receives the mission is initial position, and the position when the fly-around mission starts is final position. The optical satellite’s approach trajectory is summarized as spacecraft's Lambert trajectory optimization. Take the time of two orbital maneuvers as optimization variables, and the fuel consumption as optimization objective. Optimize the plan of orbital maneuvering. The total pulse thrust velocity required for orbital maneuver after optimization in the example is 18.2514m/s, which is highly feasible in engineering. This method can be used for space situational awareness and in-orbit services of GEO spacecraft.

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“…T HIS Note is built on previous work of developing state transition tensors for unperturbed satellite motion [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Griffith [1] explored the use of computational differentiation tool to automate up to second-order Keplerian motion sensitivities.…”

Section: Introductionmentioning

confidence: 99%

“…Kimura and Yamada [9] investigated the relative motion of spacecraft formation flying using a state transition matrix in unperturbed eccentric orbits, whereas Koenig et al [10] obtained new state transition tensors for perturbed eccentric orbits. Dang [11] developed a new state transition matrix for arbitrary Keplerian motion. Various methods have been researched to compute the accurate orbital trajectory and state transition tensors [12,13].…”

Section: Introductionmentioning

confidence: 99%