[Ether]

Originally Posted by rahilm

...you're going to be 1 processor cycle behind (time wise) on position.

Edit: This is what I mean by being 1 processor cycle behind. To integrate, you basically have to use Reimann sums in this case. For best accuracy, you'd want trapezoidal sums, so for 1 position value, you need 2 velocity values, so 3 acceleration values. This means you'd have to integrate acceleration for 2 cycles to get the two velocity values required for a single position value, putting you 1 cycle behind realtime.

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