Abstract
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.
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