Can anyone help me to solve a Control Systems problem from Controls Course?

Given the following nonlinear model, consider the output to be the radius r. Find the transfer function of the linearized model around: r = R, θ' = Ω , u=0, where R, Ω , and μ are constants.

r'' - r * θ' ^2 = - μ / r^2 + u

r * θ'' + 2 * r' + θ' = 0

Big props to whoever can walk me through how to solve this problem. Thanks!

Answer:
first you take the laplace transform of the pieces of the equation

then you linearize it by making assumptions for small disturbances in r like.. if you have a term like
sin(theta)
you would substitute that with just theta, since a very small change in theta is close to theta (in radians of course)

but from the looks of this problem, it just seems you need to take the laplace transform of the equations, making sure you know which variables depend on r, then solving for r/theta, assuming theta is the input

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Can anyone help me to solve a Control Systems problem from Controls Course?

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