I have been trying to simulate particles trapped in a parabolic potential in two dimensions. Due to the circular symmetry of the system, in the ground state at zero temperature, the particles are seen to arrange themselves in concentric rings. As I increase the temperature gradually, the expected result is to observe fluctuations about the mean position. However, due to the circular symmetry in the system, the particles are seen to undergo a body rotation. Can anyone please suggest a way to circumvent this self-rotation? It is imperative that the total energy remains constant during the simulation.