Under a microgravity condition, the microgravity-induced motion of a rigid pendulum has many special properties, which cannot be successfully revealed by any known theory. This work suggests a new fractal model for this purpose to describe the microgravity-induced motion by using the fractal derivative, and its variational principle is successfully established according to the semi-inverse method. The variational principle is very helpful to construct conservation laws and to suggest solution structures of the new fractal model. The approximate analytical solution of the model is gained by the two-scale transform method and the homotopy perturbation method.

中文翻译：

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微重力中的刚摆：一些特殊性质和两尺度分形模型

在微重力条件下，刚性摆的微重力运动具有许多特殊性质，这是任何已知理论都无法成功揭示的。本工作为此提出了一种新的分形模型，利用分形导数来描述微重力引起的运动，并根据半反演方法成功地建立了其变分原理。变分原理对于构造守恒定律和提出新分形模型的解结构非常有帮助。通过两尺度变换法和同伦摄动法得到模型的近似解析解。