By Ye Yan, Xu Huang, Yueneng Yang

ISBN-10: 9811026025

ISBN-13: 9789811026027

ISBN-10: 9811026033

ISBN-13: 9789811026034

This publication develops a dynamical version of the orbital movement of Lorentz spacecraft in either unperturbed and J2-perturbed environments. It explicitly discusses 3 forms of usual area missions regarding relative orbital keep watch over: spacecraft soaring, rendezvous, and formation flying. thus, it places ahead designs for either open-loop and closed-loop keep watch over schemes propelled or augmented by means of the geomagnetic Lorentz strength. those regulate schemes are solely novel and signify a considerably departure from prior approaches.

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**Additional info for Dynamics and Control of Lorentz-Augmented Spacecraft Relative Motion**

**Example text**

33) yields the nonlinear equations of relative orbital motion of Lorentz spacecraft expressed in the LVLH frame, given by €x ¼ 2u_ T y_ þ u_ 2T x þ €uT y þ n2T RT À n2L ðRT þ xÞ þ ax þ aR ð2:34Þ €y ¼ À2u_ T x_ þ u_ 2T y À €uT x À n2L y þ ay þ aS €z ¼ Àn2L z þ az þ aW pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ where nT ¼ l=R3T and nL ¼ l=R3L . RL ¼ ½ðRT þ xÞ2 þ y2 þ z2 1=2 is the orbital radius of Lorentz spacecraft. , jjqjj ( RL ; RT ), the above nonlinear equations can be further linearized. À3=2 %1À 3x RT ð2:35Þ By substituting Eq.

1], Copyright 2014, with permission from SAGE The orbital radius vector of the Lorentz spacecraft and the target spacecraft are, respectively, RL ¼ ½ RT þ x y z T and RT ¼ ½ RT 0 0 T . Then, the relative position vector between these two spacecraft is q ¼ RL À RT ¼ ½ x y z T . 1 State Equation of Relative Translational Motion The relative translational dynamics of Lorentz spacecraft has been detailedly discussed in Sect. 2. The equations of relative translational motion are given by €x ¼ 2u_ T y_ þ u_ 2T x þ €uT y þ n2T RT À n2L ðRT þ xÞ þ ax €y ¼ À2u_ T x_ þ u_ 2T y À €uT x À n2L y þ ay €z ¼ ð3:1Þ Àn2L z þ az pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ where nT ¼ l=R3T and nL ¼ l=R3L .

OL XBL YBL ZBL is the body frame of the Lorentz spacecraft, of which the axes are aligned with principle axes of inertial. m. of the Lorentz spacecraft. Furthermore, it is assumed that the target’s body frame is coincided with the LVLH frame. © Springer Science+Business Media Singapore 2017 Y. 1007/978-981-10-2603-4_3 35 36 3 Relative Navigation of Lorentz-Augmented Orbital Motion Fig. 1 Deﬁnitions of coordinate frames. Reprinted from Ref. [1], Copyright 2014, with permission from SAGE The orbital radius vector of the Lorentz spacecraft and the target spacecraft are, respectively, RL ¼ ½ RT þ x y z T and RT ¼ ½ RT 0 0 T .

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