I want to simulate a mechanic object like this:
init acceleration a;
init velocity v;
init position x;
loop {
get delta time dt;
v = v + a*dt;
x = x + v*dt;
}
I use the velocity (which is the derivative of position) at the end of each time step to approximate the new position. So this should be exactly what the backward euler method does.
Do I have an error in reasoning?
Assuming your acceleration is constant, you should be taking the change in velocity into account when calculating your position and therefore you should also update your position first.
Update the position using the current position (xo), the current velocity(vo), and the change in velocity due to acceleration (0.5 * a * t^2):
x = xo + vo * t + 0.5 * a * t^2 (that's delta-time squared)
Then update your velocity (which you're already doing correctly).
v = vo + a * t
This is correct mathematics, though a few things I want to point out.
A) your first position value and first velocity value from loop will always be off.
B)if the dt is near zero, or gets rounded to zero, you'll not get any correct vales.
C)you need a reimann sum, not an Euler. :-).
D) you need the program to use average velocity (dv/2) and average acceleration for correct calculations.
Try something like this:
`
Float accel, vel, pos;
Float da,dv,dx;
Loop {
Get(dT)
Get(newAccel);
da = (accel-newAccel)/dT; //FINDS da in m/s2
accel = newAccel;
dv = (da*dT)/2; //uses the average acceleration (IVT) to find dv
dx = (dv*dT)/2; //uses average change in vel (ivt) to find dx
Vel += dv; //add change in vel
Pos += dx; //add change in pos
}
