Abstract
In this paper, Smarandache trajectory curves of constant mass point particles are described and evaluated as they move along the trajectory curve in Euclidean 3-space E-3 using its position adapted frame (PAF). We also look at the Frenet apparatus of these unique trajectories. We anticipate a new way of analysing particle kinematics that could be useful in some application areas of differential geometry and particle physics. We then give a computational examples to illustrate these curves.