Lindstedt-Poincaré Series Expansion

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A high-order semi-analytical perturbation method for computing periodic orbits, quasi-periodic orbits, and their invariant manifolds near libration points. Solutions are expanded as series in amplitude parameters and phase variables, with frequency corrections determined order by order. The paper uses an order-25 procedure to directly produce high-accuracy initial conditions for invariant objects.

Application Value

The Lindstedt-Poincaré Series Expansion plays a significant role in cislunar space mission design, analysis, and control. In orbital design, it can be leveraged for transfer trajectory optimization; in navigation and control, it improves mission execution precision and reliability; in system analysis, it facilitates deeper understanding of complex multi-body dynamical behavior, guiding mission planning and risk assessment.

References

  • Low-Energy Transfers in the Earth–Moon System (Alessi et al., 2011)
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Contributors: ouyangjiahong, Ou Yang Jiahong