I have a long vector
acceleration=[6.45, 6.50, 6.52, 6.32, .... , 4.75]
Already obtained from a simulink (takes a very long time to run the simulink model again). And assume the step time is constant dt=0.1
Is there any way to find the final position numerically?
I know there is a trapz function an I know that MATLAB supports 2D integration and I know that integration inside simulink is an option. However, is there any way to take double integration:
final_position= integrate integrate acceleration dt^2
Numerically, with a precision not worse than trapezoidal method?
I prefer to avoid loop based solution.
Using the trapezoidal rule:
vinit = 0; % initial velocity
pinit = 0; % initial position
velocity = zeros(size(acceleration)) + vinit; % velocity vector
position = zeros(size(acceleration)) + pinit; % position vector
velocity(2:end) = velocity(2:end) + 0.5 * dt * cumsum(acceleration(2:end)+acceleration(1:end-1));
position(2:end) = position(2:end) + 0.5 * dt * cumsum( velocity(2:end)+ velocity(1:end-1));
I'm using cumsum() (cumulative sum) to calculate the integral at each point, not just the overall sum; this means that the velocity can be integrated again to get the position. The final position is obviously position(end).