Problem
Say I have the following equation.
$y=f(\theta)$
Where
$\theta = \int\int\alpha$
Is it possible to express the equation in terms of $\alpha$ and not the double integral of it?
Origin
This problem originates from the problem shown in the image below.
Where the equations $F_y=M_ysin(\frac{\pi}{2}-\theta)$ and $F_x=M_ycos(\frac{\pi}{2}-\theta)$ both depend on the angle $\theta$ but where only the angular acceleration $\alpha$ is known.
With the additional comments, the angular acceleration $\alpha$ is a constant (not depending of $\theta$). You can then write $$\theta=\theta_0+\omega_0t+\frac 12\alpha t^2$$ Here $\theta_0$ is the original angle of the rocket, and $\omega_0$ is the original angular velocity. $t$ is time.