I hope this is a relevant place for me to ask a math question regarding aircraft design.
I am trying to understand how one would implement a controller to control the pitch angle of an airplane for a small exercise. I understand the control part and its implementation. What I do not grasp is how one acquires the longitudinal equations of motions (which are then used for the control part) which serves as the starting point. What is the starting point or what are the principles used to derive these equations? If I know how to derive these equations for a very simple case, then I know I have to linearize the equations and then apply control theory to it.
For example, how are the left and right hand sides of eq. 4.70 from pp. 164 of the following book book is derived?
I will appreciate a simple explanation of the above case.
- I am attaching two screen shots of two sets of equations from two sources. Links to the books are included below. Both sources state these are longitudinal equations of motion although their general form differ from each other.
- I think I got to understand one point: these equations were derived considering translation motion on the x and z planes and rotation about the y axis (so stated in the first book) Thereafter, I don't understand the procedure.
1st set of equations from book 1: second set of equations from source 2: