The equations of motion of the planar elliptic restricted three-body problem are transformed to four decoupled Hill’s equations. By using the Floquet theorem, a perturbative solution to the oscillator equations with time-dependent periodic coefficients are presented. We clarify the transformation details that provide the applicability of the method. The form of newly derived equations inherently comprises the stability boundaries around the triangular Lagrangian points. The analytic approach is valid for system parameters \(0 < e \le 0.05\) and \(0 < \mu \le 0.01\) where e denotes the eccentricity of the primaries, while \(\mu \) is the mass parameter. Possible application to known extrasolar planetary systems is also demonstrated.

平面椭圆约束三体问题的运动方程被转化为四个解耦的希尔方程。通过使用Floquet定理，给出了具有时变周期系数的振动方程的摄动解。我们阐明提供该方法适用性的转换细节。新推导方程的形式固有地包含三角形拉格朗日点周围的稳定性边界。解析方法对于系统参数\（0 <e \ le 0.05 \）和\（0 <\ mu \ le 0.01 \）有效，其中e表示基元的偏心率，而\（\ mu \）是质量参数。还展示了可能应用于已知太阳系外行星系统的情况。