@Article{icces.2023.09138,
AUTHOR = {Zipu Yan, Honghua Dai, Xiaokui Yue},
TITLE = {Collocation-Based	Reconstruction	Harmonic	Balance	Method	for	Solving	 Periodic	Orbits	of	Aerospace	Vehicles},
JOURNAL = {The International Conference on Computational \& Experimental Engineering and Sciences},
VOLUME = {26},
YEAR = {2023},
NUMBER = {3},
PAGES = {1--1},
URL = {http://www.techscience.com/icces/v26n3/54059},
ISSN = {1933-2815},
ABSTRACT = {As	a	significant	research	interest	in	orbital	mechanics,	periodic	orbits	are	fundamental	for	understanding	
orbital	behaviors	and	space	explorations.	Although	the	harmonic	balance	(HB)	method	and	its	variants	have	
been	the	most	widely-used	approaches	for	periodic	dynamical	systems,	they	are	seldom	applied	to	celestial	
dynamics.	 Here	 we	 use	 the	 reconstruction	 harmonic	 balance	 (RHB)	 method	 for	 solving	 periodic	 orbits.	
Starting	 from	 a	 presupposed	 Fourier	 form	 and	 an	initial	 guess	 at	 the	 solution,	 the	 algorithm	 uses	 timedomain	 collocation	 points	 to	 optimally	 reconstruct	 the	 high-order	 HB	 procedure	 without	 complicated	
symbolic	operations	and	non-physical	solutions.	Following	a	description	of	the	method,	it	is	applied	to	two	
aerospace	 missions	 with	 nonlinear	 time-periodic	 dynamics:	 formation-flying	 and	 restricted	 three-body	
problem.	 In	 all	 cases,	 the	 RHB	 method	 can	 derive	 periodic	 solutions	 for	 the	 states,	 which	 has	 a	 semianalytical	 form	 suitable	 for	 not	 only	 further	 amplitude-frequency	 response	 analysis	 but	 online	 storage.	
Therefore,	the	method	has	clear	application	in	the	initial	reference	orbit	design	and	advanced	fuel-efficient	
aerospace	control	laws.},
DOI = {10.32604/icces.2023.09138}
}