Geometric Approaches to Lagrangian Averaging
Geometric Approaches to Lagrangian Averaging
Lagrangian averaging theories, most notably the generalized Lagrangian mean (GLM) theory of Andrews and McIntyre, have been primarily developed in Euclidean space and Cartesian coordinates. We reinterpret these theories using a geometric, coordinate-free formulation. This gives central roles to the flow map, its decomposition into mean and perturbation maps, and …