Consider a particle P that moves only on the surface of a circular cylinder r (t) = constant, it is possible to align the z axis of the fixed frame F with the axis of the cylinder. Then, the angle θ around this axis in the x – y plane can be used to define the trajectory as, r ( t ) = r cos ⁡ ⁡ ( θ θ ( t ) ) x ^ ^ + r sin ⁡ ⁡ ( θ θ ( t ) ) y ^ ^ + z ( t ) z ^ ^ , where the constant distance from the center is denoted as r, and θ (t) is a function of time.