Periodic Relative Motion Near a Keplerian Elliptic Orbit with Nonlinear Differential Gravity

Sengupta, Prasenjit; Sharma, Rajnish; Vadali, Srinivas R.

doi:10.2514/1.18344

Cited by 33 publications

(21 citation statements)

References 22 publications

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“…Since x, y, z 1, the term 1/d 3 can be expanded as a series of Legendre polynomials, as shown by Sengupta et al (2006), to yield the following system of equations:…”

Section: Nonlinear Relative Motionmentioning

confidence: 99%

“…The relative motion equations perturbed by higher-order differential gravity terms have been analyzed and solved with particular application to formation flight and periodic motion (Richardson and Mitchell 2003;Vaddi et al 2003;Gurfil 2005b;Sengupta et al 2006). By representing relative motion using spherical coordinates, and by the use of perturbation techniques, Karlgaard and Lutze (2003) solved the Clohessy-Wiltshire equations perturbed by second-order differential gravity terms with a circular reference.…”

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confidence: 99%

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Second-order state transition for relative motion near perturbed, elliptic orbits

Sengupta

Vadali

Alfriend

2006

Celestial Mech Dyn Astr

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This paper develops a tensor and its inverse, for the analytical propagation of the position and velocity of a satellite, with respect to another, in an eccentric orbit. The tensor is useful for relative motion analysis where the separation distance between the two satellites is large. The use of nonsingular elements in the formulation ensures uniform validity even when the reference orbit is circular. Furthermore, when coupled with state transition matrices from existing works that account for perturbations due to Earth oblateness effects, its use can very accurately propagate relative states when oblateness effects and second-order nonlinearities from the differential gravitational field are of the same order of magnitude. The effectiveness of the tensor is illustrated with various examples.

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“…Since x, y, z 1, the term 1/d 3 can be expanded as a series of Legendre polynomials, as shown by Sengupta et al (2006), to yield the following system of equations:…”

Section: Nonlinear Relative Motionmentioning

confidence: 99%

mentioning

confidence: 99%

Second-order state transition for relative motion near perturbed, elliptic orbits

Sengupta

Vadali

Alfriend

2006

Celestial Mech Dyn Astr

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“…(34), Sengupta et al (2006) gave an exact particular integral solution about the true anomaly. Herein, our purpose is to obtain the second-order state transition equations from Eqs.…”

Section: Solution Of Second-order State Transition Equationsmentioning

confidence: 95%

“…Higherorder nonlinearities were treated as forcing functions on the linear system by Euler and Shulman (1967) and by Sengupta et al (2006). By representing the relative motion with a circular reference orbit in terms of the relative spherical coordinates and using the perturbation technique, Karlgaard and Lutze (2003) solved the HCW equations perturbed by second-order differential gravity terms.…”

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confidence: 99%

A second-order solution to the two-point boundary value problem for rendezvous in eccentric orbits

Zhang

Zhou

2010

Celest Mech Dyn Astr

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A new second-order solution to the two-point boundary value problem for relative motion about orbital rendezvous in one orbit period is proposed. First, nonlinear differential equations to describe the relative motion between a chaser and a target are presented considering the second-order terms in the gravity. Then, by regarding the second-order terms as external accelerations, we establish second-order state transition equations. Moreover, the J2 perturbations effects can also be considered in the state transition equations. Last, the initial relative velocity to fulfill a rendezvous is determined by solving the state transition equations. Numerical simulations show that the new second-order state transition equations are accurate. The second-order solution to the two-point boundary value problem on eccentric orbits is valid even if the relative range is farther than 500 km.

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“…In the case of a circular reference orbit, initial conditions that are expressed in terms of the Hill coordinates have already been derived for canceling the effects of J 2 (2) . Even in the case of an elliptic reference orbit, the initial conditions for canceling the effects of J 2 have been derived (3) ; however, the initial velocities are not expressed in terms of the time derivatives of the Hill coordinates, and thus, they are not necessarily suitable as the initial conditions for the deputy spacecraft. In this study, the initial velocity of the deputy spacecraft for canceling the effects of J 2 are derived in terms of…”

Section: Introductionmentioning

confidence: 99%

Effects of Perturbation on Formation Flights around an Eccentric Reference Orbit

Yamada

Shima

Yoshikawa

2008

JSE

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In this study, we propose a basic method for the construction of a formation flight around an eccentric reference orbit under the influence of gravitational disturbances (J 2 ). The relative motion between two spacecraft in the formation flight is affected by J 2 . The effects of this perturbing force are analyzed, and the initial conditions of the formation flight for the suppression of these effects are derived on the basis of these analytical results. r : position vector of the spacecraft in the inertial system u : velocity vector of the spacecraft in the inertial system a : semimajor axis of the (chief) reference orbit e : eccentricity of the reference orbit i : inclination of the reference orbit ω : argument of the perigee of the reference orbit Ω : right ascension of the reference orbit M : mean anomaly of the chief spacecraft E : eccentric anomaly of the chief spacecraft ν : true anomaly of the chief spacecraft θ : true latitude of the chief spacecraft (θ = ν + ω) q 1 , q 2 : components of the eccentricity vector (q 1 = e cos ω, q 2 = e sin ω) n : mean orbit rate Subscripts c and d indicate the variables of chief spacecraft and deputy spacecraft, respectively.

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Periodic Relative Motion Near a Keplerian Elliptic Orbit with Nonlinear Differential Gravity

Cited by 33 publications

References 22 publications

Second-order state transition for relative motion near perturbed, elliptic orbits

Second-order state transition for relative motion near perturbed, elliptic orbits

A second-order solution to the two-point boundary value problem for rendezvous in eccentric orbits

Effects of Perturbation on Formation Flights around an Eccentric Reference Orbit

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