theory of manifolds

According to the stability region theory of constrained dynamic system, the restricted stability boundary is composed of stable manifolds of unstable equilibrium points, periodic orbits and semi-saddles on the boundary, and portions of the boundary of the feasible region.

根据带约束动力系统稳定域理论，其受限稳定边界由边界上不稳定平衡点、周期轨和半鞍点的稳定流形以及部分可行域边界构成。

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The equations are approximately solved by nonlinear normal modes ( NLNM) superposition method based on the theory of Shaw invariant manifolds. The solutions using nonlinear normal modes superposition and direct numerical methods are simulated respectively, and the feasibility is validated by comparing the results.

论文采用Shaw不变流形法对模型运动微分方程组进行了非线性模态叠加近似求解，并对模态叠加解与直接数值解进行了仿真，对比结果验证了该方法的可行性。

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According to the theory of nonlinear dynamic system, the stability boundary is the union of the stable manifolds of the equilibrium points on the stability boundary.

依据非线性动力系统理论，稳定域边界应由其所有不稳定平衡点的稳定流形的并集构成。

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