To overcome this difficulty, some variants of the Verlet algorithm have been developed. They give rise to exactly the same trajectory, and the stored variables are different in memory and at what times. The leap frog algorithm(191) (Equation 3.8) is one of such variants where velocities are handled somewhat well. In this algorithm, the velocities are first calculated from and then used to calculate the position x at time . The velocities at time t can then be approximated by Equation 3.8.