We have a Newtonian physics simulation with a state matrix containing the instantaneous velocities, angular velocities, positions and orientations of an object ; and we apply classical Runge-Kutta 4 method to advance step by step in the simulation.
For now, at each step, we compute the new velocities and the new position/orientation at once multiplying our state-derivative matrix with RK4 timesteps and half-timesteps.
I was wondering if and why RK4 with 2nd-derivative would give more precise results. As we compute all necessary linear and angular accelerations in the process, we could easily switch to 2nd-derivative RK4.
I hope I gave enough details, I can give more if necessary.
Thanks in advance!