Let's get to the basic physics of flying using a thrust that is less than the weight of the body. It's not only possible, but it's so natural that we should actually ask why do we need any thrust at all!
Presenting some of the stories that have been closest to my heart, most of them from my childhood. Each of these may or may not be from a Vedantic text - if not - it's still here because it's close to the idea of Vedanta, and because it's inspirational for Vedantins.
Also, these are my own renderings of the stories. So I need to disclaim any authenticity - the stories presented here can be quite different from their original versions whatever may those be.