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The integrals of the motion take the form 

From (2.5), (2.6) and (2.7) we find 

<img src='content_image/361590.jpg'>

<img src='content_image/361591.jpg'>

<img src='content_image/361592.jpg'>

We point out that the “+” and “ − ” signs correspond to the two possible orientations of the angular momentum. We choose, without loss of generality, the sign “+” and J > 0 throughout this work. Now, from Eq. (2.8) we find that the trajectories should satisfy 

<img src='content_image/361588.jpg'>

and we can classify the types of motion as folows. The first two possibilities refer to J ̸ = 0. Namely, 

<img src='content_image/361587.jpg'>

where ω = c R = κ $^{2}$R p 0 = c √ 3 κ 2 2 E . So in this case we have a uniform motion in a circle with the linear speed | v | = ωR = c . This solution can also be obtained from Eq. (2.2) by demanding x$_{·}$p = 0. Indeed, it can be easily checked that (2.2) and (2.3) imply the system 

From (2.11) it follows easily that the orthogonality of x and p refers to the motion of a particle in a circle with radius | x | = R = √ 2 E 3 κ 2 . κ 2 

2) For r ( E − 2 r 2 ) > Jc , the path lies entirely within the annulus bounded by the circles r = r$_{min}$ and r = r$_{max}$ , that is we have 

<img src='content_image/361586.jpg'>

<img src='content_image/361585.jpg'>

