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I'm currently doing some mathematical modelling at my work, and I have arrived at an interesting kind of circular relationship integral - and now I'm wondering about what to do.

The integral looks very innocent at first glance:

$$ \theta_s = \int\limits_0^{t_1} \omega (t) dt$$

So, it's a circular rotating body, with some time-dependent angular velocity. However, the ##\theta_s## is a constant - a parameter we can design in the system.

But what makes the thing complex (at least in my head) is that ##t_1## is the time it takes for the body to rotate the amount ##\theta_s## - so the upper limit becomes dependent on the angular velocity also.

Can I create another integral that relates the time ##t_1## to ##\omega (t)## and ##\theta_s##?

Is Leibniz' rule the way to go?

And ##\omega (t)## is an unknown function, by the way.

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# I Some weird circular relationship

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