# Computer Animation and Euler-Integration

What is integrated with the Euler integration?

IMHO: integration to obtain the velocity at time t to a place. Acceleration a is constant over time interval t. Right?

S(t0 -> delta_t) = S0(t) + ∫ s'(t) dt

s'(t) is derivated S

Please see Tim van Beek Answer. It's the right one :)

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ah damn: i forgot to tell: S(t) is the place in time t –  RenHoek Aug 2 '11 at 13:08
We aren't clairvoyant; if you're working with a computer animation that integrates velocity to obtain position, then that's what you're doing, if that's not what you're integrating, then that's not what you're doing - how are we supposed to know without ESP? How are we supposed to know if the acceleration of something you're working with is constant if we don't have access to it and you're not telling us anything about it? Also, you can edit your own question, which is better than adding information in comments. You have to understand: people can only help you if you communicate. –  anon Aug 2 '11 at 13:27
@RenHoek: As it stands, it is quite impossible to answer your question. Can you exapnd it to include a description of what you want? –  Mariano Suárez-Alvarez Aug 2 '11 at 14:12
@anon that was what i had :( i can't give mire information then i have ... but Tim understood my partial Informtaion.... –  RenHoek Aug 2 '11 at 17:10

If you are further talking about Newtonian mechanics, you mean that there is a point mass of mass $m$ whose behaviour is described by the equation $$F = m * a$$ Force = mass times accelaration. This is an ordinary differential equation of second order for the position of the point mass as a function of time $t$, $S(t)$, because we have $$S''(t) = a(t)$$ that is the first derivative of $S$ is the velocity $v(t)$, and the second is the acceleration $a(t)$. In order to get a unique solution, we need to specify initial conditions for both $S(t)$, $$S(t =0) = S_0$$ which is the initial position and for $v(t)$, $$v(t = 0) = v_0$$ which is the initial velocity of the point mass. Now you can prescribe the force $F(t)$ as a differentiable function of time and calculate the position $S(t)$ numerically using the Euler method. If you set the force to zero, then you have zero acceleration and the unique solution in closed form is $$S(t) = S_0 + v_0 t$$ In this case the numerical approximation via the Euler method will coincide with the solution obtained in closed form. But in general there will be an approximation error.