This work represents a survey of results on roulettes of conics and Delaunay surfaces. The differential equations corresponding to roulettes of conics appear scarcely in the literature, and their real-world applications are also emphasized way too rarely. The purpose of this survey is to make the connection between all these topics a lot more obvious and relevant. In the last section, we construct an extension of an example provided by Thomas Vogel, on the topic of liquid bridges as Delaunay rotational surfaces. We model this application using numerical methods.

Delaunay surfaces, liquid bridges between vertical plates.