A Series Solution to the Stark Dynamics in the Circular Restricted Three-body Problem

Ke Li; Haibin Shang; Yue Dong; Lusha Shi

doi:10.1016/j.ifacol.2025.11.355

A Series Solution to the Stark Dynamics in the Circular Restricted Three-body Problem

Ke Li^*
, Haibin Shang^*
, Yue Dong^*
, Lusha Shi

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

Abstract

The Stark problem is a topic of interest in orbital mechanics due to its potential applications in trajectory design. In this paper, the Stark problem under the Circular Restricted Three-Body Problem is investigated, and a semi-analytical series method is proposed for its solution. The Taylor series is employed to expand the dynamics of the massless particle. Recursive formulas for the series coefficients are constructed to accelerate the computation of high-order derivatives. Sundman transformations are incorporated to enhance propagation performance. Numerical simulations demonstrate that selecting appropriate Sundman transformation types and the expansion order enables efficient propagation of trajectories for the Stark problem in the CRTBP.

Original language	English
Pages (from-to)	1416-1421
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	59
Issue number	20
DOIs	https://doi.org/10.1016/j.ifacol.2025.11.355
Publication status	Published - 1 Aug 2025
Externally published	Yes
Event	23th IFAC Symposium on Automatic Control in Aerospace, ACA 2025 - Harbin, China Duration: 2 Aug 2025 → 6 Aug 2025

Keywords

Circular Restricted Three-Body Problem
F and G series
Stark problem
Sundman transformation
Trajectory propagation

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10.1016/j.ifacol.2025.11.355

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title = "A Series Solution to the Stark Dynamics in the Circular Restricted Three-body Problem",

abstract = "The Stark problem is a topic of interest in orbital mechanics due to its potential applications in trajectory design. In this paper, the Stark problem under the Circular Restricted Three-Body Problem is investigated, and a semi-analytical series method is proposed for its solution. The Taylor series is employed to expand the dynamics of the massless particle. Recursive formulas for the series coefficients are constructed to accelerate the computation of high-order derivatives. Sundman transformations are incorporated to enhance propagation performance. Numerical simulations demonstrate that selecting appropriate Sundman transformation types and the expansion order enables efficient propagation of trajectories for the Stark problem in the CRTBP.",

keywords = "Circular Restricted Three-Body Problem, F and G series, Stark problem, Sundman transformation, Trajectory propagation",

author = "Ke Li and Haibin Shang and Yue Dong and Lusha Shi",

note = "Publisher Copyright: Copyright {\textcopyright} 2025 The Authors.; 23th IFAC Symposium on Automatic Control in Aerospace, ACA 2025 ; Conference date: 02-08-2025 Through 06-08-2025",

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T1 - A Series Solution to the Stark Dynamics in the Circular Restricted Three-body Problem

AU - Li, Ke

AU - Shang, Haibin

AU - Dong, Yue

AU - Shi, Lusha

PY - 2025/8/1

Y1 - 2025/8/1

N2 - The Stark problem is a topic of interest in orbital mechanics due to its potential applications in trajectory design. In this paper, the Stark problem under the Circular Restricted Three-Body Problem is investigated, and a semi-analytical series method is proposed for its solution. The Taylor series is employed to expand the dynamics of the massless particle. Recursive formulas for the series coefficients are constructed to accelerate the computation of high-order derivatives. Sundman transformations are incorporated to enhance propagation performance. Numerical simulations demonstrate that selecting appropriate Sundman transformation types and the expansion order enables efficient propagation of trajectories for the Stark problem in the CRTBP.

AB - The Stark problem is a topic of interest in orbital mechanics due to its potential applications in trajectory design. In this paper, the Stark problem under the Circular Restricted Three-Body Problem is investigated, and a semi-analytical series method is proposed for its solution. The Taylor series is employed to expand the dynamics of the massless particle. Recursive formulas for the series coefficients are constructed to accelerate the computation of high-order derivatives. Sundman transformations are incorporated to enhance propagation performance. Numerical simulations demonstrate that selecting appropriate Sundman transformation types and the expansion order enables efficient propagation of trajectories for the Stark problem in the CRTBP.

KW - Circular Restricted Three-Body Problem

KW - F and G series

KW - Stark problem

KW - Sundman transformation

KW - Trajectory propagation

UR - https://www.scopus.com/pages/publications/105025983296

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DO - 10.1016/j.ifacol.2025.11.355

M3 - Conference article

AN - SCOPUS:105025983296

SN - 2405-8963

VL - 59

SP - 1416

EP - 1421

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 20

T2 - 23th IFAC Symposium on Automatic Control in Aerospace, ACA 2025

Y2 - 2 August 2025 through 6 August 2025

ER -

A Series Solution to the Stark Dynamics in the Circular Restricted Three-body Problem

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