[Ether]

Originally Posted by Ether

Assuming that X₀ and V₀ are given, and assuming that the update period dt is short enough that the acceleration is accurately approximated as a linear function of time, then the position is given by:

X₁ = X₀ + dt*V₀ + dt²*(a₁ + 2*a₀)/6

X₂ = X₁ + dt*V₁ + dt²*(a₂ + 2*a₁)/6

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X_n = X_n-1 + dt*V_n-1 + dt²*(a_n + 2*a_n-1)/6

I forgot to post the computation for Vn:

V_n = V_n-1 + dt*(a_n+a_n-1)/2