提出了构造一类非线性振子解析逼近周期解的的初值变换法。用Ritz-Galerkin法，将描述动力系统的二阶常微分方程，化为以振幅、角频率和偏心距为独立变量的不完备非线性代数方程组；关键是考虑初值变换,增加补充方程，构成了以角频率、振幅和偏心距为变量的完备非线性代数方程组。作为例子利用初值变换法求解了相对论修正轨道方程的六种分岔周期解。给出了非对称振动的幅频曲线和偏频（偏心距与角频率的关系）曲线。发现了固有角频率漂移现象。

The periodic solutions of a class of nonlinear oscillators can be expressed in the forms of basic harmonics and bifurcate harmonics. Thus, an oscillation system which is described as a second order ordinary differential equation, can be expressed as a set of non-linear algebraic equations with frequency, central offset and amplitudes as the independent variables by using Ritz-Galerkin method. But the set of equations is incomplete. The key is that considering initial -value transformation, supplementary equations. were added and a set of non-linear algebraic equations with angular frequencies and amplitudes as the independent variables was constituted completely. As examples, six asymmetric periodic solutions bifurcating about a nonlinear differential equation arising in general relativity were solved by using the method of initial-value transformation. Amplitude-frequency curves and central offset-frequency curves of the asymmetrical vibration systems were derived. In addition, the drift phenomenon of natural angular frequency was discovered.