Work with Ross Hatton. Keywords: locomotion, snake robots, gait design Abstract: Animals often use gaits — cyclic changes in shape producing a net displacement — to move through their environments. In robotics, we are interested in planning motions for artificial systems that can match or exceed the locomotive capabilities of animals. A fundamental question of locomotion is "What are the characteristics of a useful gait?" The geometric mechanics community has made significant progress in answering this question, identifying functions of the system shape that capture the net displacements induced by broad classes of gaits without having to individually test each possible motion. In this talk, we first introduce these results with the aim of separating them from the specialized language of differential geometry and making them accessible to a broader audience. Following this introduction, we then examine how the choice of generalized coordinates quality of the locomotion functions, a question which has not previously been addressed.