# Integration when some of the values change over time

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L'O.G. am 11 Mai 2023
Kommentiert: Torsten am 11 Mai 2023
I have a function of the form where is the position of the k-th object and is the corresponding force. The force has a functional that is also dependent on . I want to integrate this with respect to time and output the value for each time point. I think the values and would therefore change as a function of time. How do I do this which I imagine would need to be done recursively?
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Torsten am 11 Mai 2023
How do you determine xk ? x can be considered as a constant during time integration ?

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### Antworten (1)

Sulaymon Eshkabilov am 11 Mai 2023
Simply write a code, e.g.:
t=linspace(0, 5, 200);
F = 5*cos(2*pi*t);
xk = 2*sin(2*pi*5*t);
x = linspace(0,25);
for ii = 1:numel(x)
y(ii) = sum((F.*(x(ii)-xk))/norm(x(ii)-xk));
end
subplot(211)
plot(xk, F)
xlabel('x_k')
ylabel('F_k')
grid on
subplot(212)
plot(x, y)
xlabel('x')
ylabel('y')
grid on
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Sulaymon Eshkabilov am 11 Mai 2023
sum() is integrating
L'O.G. am 11 Mai 2023
y(x) is defined via a sum. As I mentioned in my post, I want to integrate over that. The confusion for me is to do so while updating the values of x_k (and hence y(x) and F_k).

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