Using Newton's method to search for quasi-periodic relative satellite motion based on nonlinear Hamilton models

V. M. Becerra; J. D. Biggs; S. J. Nasuto; V. F. Ruiz; W. Holderbaum; D. Izzo

Using Newton's method to search for quasi-periodic relative satellite motion based on nonlinear Hamilton models

V. M. Becerra, J. D. Biggs, S. J. Nasuto, V. F. Ruiz, W. Holderbaum, D. Izzo

Research output: Contribution to conference › Paper › peer-review

Abstract

In this paper, the monodromy variant of Newton’s method is applied to locate periodic or quasi-periodic relative satellite motion. Advantages of using Newton’s method to search for periodic or quasi-periodic relative satellite motion include simplicity of implementation, ability to deal with nonlinear dynamics, repeatability of the solutions due to its non-random nature, and fast convergence. A nonlinear Hamiltonian model is derived which incorporates eccentricity of the reference orbit, nonlinear gravitational terms and the J₂ perturbation. Closed-loop control of relative satellite motion is simulated with the aid of a discrete LQR controller with impulsive actuation.

Original language	English
Pages	193 - 202
Publication status	Published - 2006
Event	7th Cranfield Conference on Dynamics and Control of Systems and Structures in Space - Cranfield University, Cranfield, United Kingdom Duration: 1 Jan 2006 → …

Conference

Conference	7th Cranfield Conference on Dynamics and Control of Systems and Structures in Space
Country/Territory	United Kingdom
City	Cranfield
Period	1/01/06 → …

Access to Document

http://centaur.reading.ac.uk/14976/

Cite this

Becerra, V. M., Biggs, J. D., Nasuto, S. J., Ruiz, V. F., Holderbaum, W., & Izzo, D. (2006). Using Newton's method to search for quasi-periodic relative satellite motion based on nonlinear Hamilton models. 193 - 202. Paper presented at 7th Cranfield Conference on Dynamics and Control of Systems and Structures in Space, Cranfield, United Kingdom. http://centaur.reading.ac.uk/14976/

@conference{cc4bec5c359944b8b146c67307ca7914,

title = "Using Newton's method to search for quasi-periodic relative satellite motion based on nonlinear Hamilton models",

abstract = "In this paper, the monodromy variant of Newton{\textquoteright}s method is applied to locate periodic or quasi-periodic relative satellite motion. Advantages of using Newton{\textquoteright}s method to search for periodic or quasi-periodic relative satellite motion include simplicity of implementation, ability to deal with nonlinear dynamics, repeatability of the solutions due to its non-random nature, and fast convergence. A nonlinear Hamiltonian model is derived which incorporates eccentricity of the reference orbit, nonlinear gravitational terms and the J2 perturbation. Closed-loop control of relative satellite motion is simulated with the aid of a discrete LQR controller with impulsive actuation.",

author = "Becerra, {V. M.} and Biggs, {J. D.} and Nasuto, {S. J.} and Ruiz, {V. F.} and W. Holderbaum and D. Izzo",

year = "2006",

language = "English",

pages = "193 -- 202",

note = "7th Cranfield Conference on Dynamics and Control of Systems and Structures in Space ; Conference date: 01-01-2006",

}

Becerra, VM, Biggs, JD, Nasuto, SJ, Ruiz, VF, Holderbaum, W & Izzo, D 2006, 'Using Newton's method to search for quasi-periodic relative satellite motion based on nonlinear Hamilton models', Paper presented at 7th Cranfield Conference on Dynamics and Control of Systems and Structures in Space, Cranfield, United Kingdom, 1/01/06 pp. 193 - 202. <http://centaur.reading.ac.uk/14976/>

Using Newton's method to search for quasi-periodic relative satellite motion based on nonlinear Hamilton models. / Becerra, V. M.; Biggs, J. D.; Nasuto, S. J. et al.
2006. 193 - 202 Paper presented at 7th Cranfield Conference on Dynamics and Control of Systems and Structures in Space, Cranfield, United Kingdom.

Research output: Contribution to conference › Paper › peer-review

TY - CONF

T1 - Using Newton's method to search for quasi-periodic relative satellite motion based on nonlinear Hamilton models

AU - Becerra, V. M.

AU - Biggs, J. D.

AU - Nasuto, S. J.

AU - Ruiz, V. F.

AU - Holderbaum, W.

AU - Izzo, D.

PY - 2006

Y1 - 2006

N2 - In this paper, the monodromy variant of Newton’s method is applied to locate periodic or quasi-periodic relative satellite motion. Advantages of using Newton’s method to search for periodic or quasi-periodic relative satellite motion include simplicity of implementation, ability to deal with nonlinear dynamics, repeatability of the solutions due to its non-random nature, and fast convergence. A nonlinear Hamiltonian model is derived which incorporates eccentricity of the reference orbit, nonlinear gravitational terms and the J2 perturbation. Closed-loop control of relative satellite motion is simulated with the aid of a discrete LQR controller with impulsive actuation.

AB - In this paper, the monodromy variant of Newton’s method is applied to locate periodic or quasi-periodic relative satellite motion. Advantages of using Newton’s method to search for periodic or quasi-periodic relative satellite motion include simplicity of implementation, ability to deal with nonlinear dynamics, repeatability of the solutions due to its non-random nature, and fast convergence. A nonlinear Hamiltonian model is derived which incorporates eccentricity of the reference orbit, nonlinear gravitational terms and the J2 perturbation. Closed-loop control of relative satellite motion is simulated with the aid of a discrete LQR controller with impulsive actuation.

M3 - Paper

SP - 193

EP - 202

T2 - 7th Cranfield Conference on Dynamics and Control of Systems and Structures in Space

Y2 - 1 January 2006

ER -

Using Newton's method to search for quasi-periodic relative satellite motion based on nonlinear Hamilton models

Abstract

Conference

Access to Document

Fingerprint

Cite this