bouncing ball

I worked on the weekend on making a toy problem for testing physics-related machine-learning methods: A ball bouncing off an elastic surface, under gravity. Both the surface and the gravity vector break the symmetry; this problem is not at all invariant with respect to rotation, translation, or boost. And yet the laws of physics can be written in a coordinate-free form. I am trying to figure out whether we can make this distinction usefully in the literature: The distinction between coordinate-free and equivariant. I think they are different concepts, even though the mathematics of them are identical.