The interest to research docking mechanisms has been increasing in the recent years, due to various reasons, e.g., On-Orbit Servicing (OOS), autonomous docking. OOS is concerned with extension of the life-time of the already flying in-orbit satellites, as well as the de-orbiting of the dead satellites, to decrease space debris. In this paper, we study a docking mechanism of a probe-drogue (cone-shaped), without any compliances between two small (<1 ton) satellites. Hard impacts are one of the main concerns during the docking process, especially for the non-compliant docking mechanism. Hence, we pay attention on contact modeling, by implementing a nonlinear contact model. In this paper, we present our 6 Degrees-of-Freedom (DoF) multibody docking model. We discuss how the 6DoF modeling is carried out using the selected nonlinear contact model. Moreover, we analyze different key parameters of our model, which affect the result of each docking scenario, in the interest of finding the worst-case scenario in terms of these key parameters. After varying these key parameters, for different docking scenarios, we define the worst-case docking scenario of our docking model, as well as the range of acceptable docking scenarios. Afterwards, we select the worst-case scenario as our docking test-case. In this paper, it is also of our interest to find out the forces and the torques that each spacecraft has to undergo during the docking process. Therefore, the results of the simulation presented in this paper, show the forces and torques acting on each spacecraft, as well as the dynamic and energy analysis of each spacecraft throughout the docking process of this test-case. Finally, we compare the docking simulation results using two different contact models; the nonlinear selected "Flores" model, and the Hertz contact model, in order to see the effect of utilizing a nonlinear contact.