Ice skating is a dynamic, creative movement with many possible gaits. There are some, but not many examples of ice skating robots, and even fewer ice skating bipedal robots. For bipedal robotic locomotion, there are standard canonical simple models such as the spring loaded inverted pendulum (SLIP model) and the compass model, which are used to analyze the simplest cases of walking and running. However, for ice skating on a surface, these models are insufficient for generating skating gaits of the kind used by humans. Using a simple controllable non-holonomic model of an ice skate that can slide along a single direction, with friction in the perpendicular direction, we demonstrate how we can use trajectory optimization to generate skating gaits. Additionally we use a hybrid trajectory optimization framework to generate gaits on a simulated bipedal robot.