Canonical modelling of relative spacecraft motion via epicyclic orbital elements

N. Jeremy Kasdin; Pini Gurfil

Canonical modelling of relative spacecraft motion via epicyclic orbital elements

N. Jeremy Kasdin, Pini Gurfil

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

This paper presents a Hamiltonian approach to modelling relative spacecraft motion based on a derivation of canonical coordinates for the relative statespace dynamics. The Hamiltonian formulation facilitates the modelling of high-order terms and orbital perturbations within the context of the Clohessy- Wiltshire solution. First, the Hamiltonian is partitioned into a linear term and a high-order term. The Hamilton-Jacobi equations are solved for the linear part by separation, and new constants for the relative motions are obtained, called epicyclic elements. The influence of higher order terms and perturbations, such as Earth's oblateness, are incorporated into the analysis by a variation of parameters procedure. As an example, closed-form solutions for J₂-invariant orbits are obtained.

Original language	English (US)
Title of host publication	AIAA Guidance, Navigation, and Control Conference and Exhibit
State	Published - 2003
Event	AIAA Guidance, Navigation, and Control Conference and Exhibit 2003 - Austin, TX, United States Duration: Aug 11 2003 → Aug 14 2003

Publication series

Name	AIAA Guidance, Navigation, and Control Conference and Exhibit

Other

Other	AIAA Guidance, Navigation, and Control Conference and Exhibit 2003
Country/Territory	United States
City	Austin, TX
Period	8/11/03 → 8/14/03

All Science Journal Classification (ASJC) codes

Aerospace Engineering
Control and Systems Engineering
Electrical and Electronic Engineering

Cite this

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title = "Canonical modelling of relative spacecraft motion via epicyclic orbital elements",

abstract = "This paper presents a Hamiltonian approach to modelling relative spacecraft motion based on a derivation of canonical coordinates for the relative statespace dynamics. The Hamiltonian formulation facilitates the modelling of high-order terms and orbital perturbations within the context of the Clohessy- Wiltshire solution. First, the Hamiltonian is partitioned into a linear term and a high-order term. The Hamilton-Jacobi equations are solved for the linear part by separation, and new constants for the relative motions are obtained, called epicyclic elements. The influence of higher order terms and perturbations, such as Earth's oblateness, are incorporated into the analysis by a variation of parameters procedure. As an example, closed-form solutions for J2-invariant orbits are obtained.",

author = "Kasdin, {N. Jeremy} and Pini Gurfil",

year = "2003",

language = "English (US)",

isbn = "9781563479786",

series = "AIAA Guidance, Navigation, and Control Conference and Exhibit",

booktitle = "AIAA Guidance, Navigation, and Control Conference and Exhibit",

note = "AIAA Guidance, Navigation, and Control Conference and Exhibit 2003 ; Conference date: 11-08-2003 Through 14-08-2003",

}

TY - GEN

T1 - Canonical modelling of relative spacecraft motion via epicyclic orbital elements

AU - Kasdin, N. Jeremy

AU - Gurfil, Pini

PY - 2003

Y1 - 2003

N2 - This paper presents a Hamiltonian approach to modelling relative spacecraft motion based on a derivation of canonical coordinates for the relative statespace dynamics. The Hamiltonian formulation facilitates the modelling of high-order terms and orbital perturbations within the context of the Clohessy- Wiltshire solution. First, the Hamiltonian is partitioned into a linear term and a high-order term. The Hamilton-Jacobi equations are solved for the linear part by separation, and new constants for the relative motions are obtained, called epicyclic elements. The influence of higher order terms and perturbations, such as Earth's oblateness, are incorporated into the analysis by a variation of parameters procedure. As an example, closed-form solutions for J2-invariant orbits are obtained.

AB - This paper presents a Hamiltonian approach to modelling relative spacecraft motion based on a derivation of canonical coordinates for the relative statespace dynamics. The Hamiltonian formulation facilitates the modelling of high-order terms and orbital perturbations within the context of the Clohessy- Wiltshire solution. First, the Hamiltonian is partitioned into a linear term and a high-order term. The Hamilton-Jacobi equations are solved for the linear part by separation, and new constants for the relative motions are obtained, called epicyclic elements. The influence of higher order terms and perturbations, such as Earth's oblateness, are incorporated into the analysis by a variation of parameters procedure. As an example, closed-form solutions for J2-invariant orbits are obtained.

UR - http://www.scopus.com/inward/record.url?scp=84896693914&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84896693914&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84896693914

SN - 9781563479786

SN - 9781624100901

T3 - AIAA Guidance, Navigation, and Control Conference and Exhibit

BT - AIAA Guidance, Navigation, and Control Conference and Exhibit

T2 - AIAA Guidance, Navigation, and Control Conference and Exhibit 2003

Y2 - 11 August 2003 through 14 August 2003

ER -

Canonical modelling of relative spacecraft motion via epicyclic orbital elements

Abstract

Publication series

Other

All Science Journal Classification (ASJC) codes

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