In this paper, the Lagrangian mathematical equation is used to construct a feature extraction model for the flexibility of aerobics athletes. At the same time, this paper uses machine vision to identify and extract feature points of aerobics movements. This paper realizes image feature recognition through multi-dimensional pixel information decomposition. At the same time, we realize the radian trajectory positioning of the aerobics action image based on the Lagrangian equation. The experimental research shows that the algorithm proposed in this paper has higher accuracy and better localization performance when recognizing the radian trajectory of aerobics movements. The algorithm improves the optimization and correction ability of aerobics movements.