How do I find the integral of a derivative that has been squared? (i.e. ∫(dy/dx)^2 dx) An example would be integrating velocity squared, with respect to time.
Well, specifically, I want to integrate this equation:
(Where θ_2 with two dots is an angular acceleration, θ_2 with one dot is an angular velocity, θ_1 and θ_2 are angles, and g, l_1, and l_2 are constants)
It is an equation of motion for a double pendulum. I want to be able to integrate it numerically between two time values so that I get the total angle moved by a pendulum arm over that time period. I have only learned a little integration, so I am quite lost as to how to do this. The squared angular velocity is my biggest difficulty, as I'd like to be able to integrate that term to have an angle as a result. Also, I am confused as to how I would deal with the angles in the equation, because they are variables and would have different values at every time. Would I just input the angles at t_1 and the angles at t_2 and do the subtraction? I'm not sure if what I want to do is even possible, but any help is much appreciated!