Lagrangian mechanics VS Newtonian Mechanics for control systems? I have seen that a lot of people doing Lagrangian mechanics that Newtonian mechanics. But I wonder if it's better to build Langarian ODE:s insted of Newtonian ODE:s if I'm going to create models of robotic arms? My goal is to build advanced mathematical models, such as robotic arms and system who have no and endpoint, of ODE:s and apply them into a linear control system. I always have the issue that I need to have stiffness $k$, like a spring, in my system, or else the system will be unstable. I inverted pendulum doesn't have stiffness in the rotating center down below. Which one is best for me then: 1. Lagrangian mechanics 2. Newtonian mechanics I have heard that Hamiltonian mechanics is used too, but they isn't fitt for control system, right? I appreciate for the answers.

Both the Lagrangian and Newtonian method should result in the same equations of motion. The only difference is how you derive them. I find that Newtonian mechanics can be a bit more intuitive, however Lagrangian mechanics is a more systematic approach and therefore less prone for errors. Especially when dealing with systems with rotational motion, like your robot arm, Newtonian mechanics can be a real pain, so I would suggest Lagrangian mechanics. But you could always do both and compare the two to be more confident about the correctness of your model.