Simplified equations for object trajectories in rotating space habitats and space juggling

Rotating space habitats provide artificial gravity as a physiological countermeasure for long-term space habitation, though the lived experience of a person in these habitats requires further investigation. Movement planning will require adaptation to the Coriolis and centrifugal forces. The multicultural arts of juggling may offer potential psycho-physiological countermeasures for some individuals and provide interesting insights into movement planning and arts in both microgravity and rotating habitats. Previously developed equations of motion for thrown objects in rotating habitats have not been centered within the lived rotating environment. Here, I show a set of simplified equations for object trajectories in rotating environments and their underlying mathematical framework. The full set of possible trajectories for objects thrown in rotating environments is provided and a simplified approach to the Coriolis and centrifugal force differential equation using complex algebra is demonstrated. Experimentation reported in this article was conducted on parabolic flights and an analog weightlessness and rotating apparatus. Near the surface of the Earth, thrown objects travel along parabolas. In rotating space environments, thrown objects will travel along a set of mathematical curves known as roulettes, created by a fixed circle and rolling line with generator point connected to the line. These roulette trajectories will be the everyday experience of every person living in a rotating space habitat, always.