Lagrange’s Equation Method | Simulations | Machine Dynamics | Mechatronic Design | LUT University

Course: Machine Dynamics 1

[leonidchechurin]

I would have pointed out maybe the main and fundamental advantage of Lagrange principle. It helps to derive CORRECT equations of a system we analyse even if it has nonlinearities or, even worse, time variant parameters. Starting from energies and taking derivatives is safe - you will get some terms in your final "Newton-like equation" that you never expected. For examples, some terms that contain derivatives of the parameter. There is no way to get the same starting with Newtonian balance of forces, simply because we do not know that those forces exist. This is how "gyroscopic" forces or "Coriolis forces" can be nicely derived from Lagrange principle proudly explaining the results of experiments, for example. All in one... I would NOT give the impression to the student that well, it is UP TO YOU which method to use, just MAYBE Lagrange is easier for multibody. It is dangerous. In 5:45 it is not PREFERABLE to choose Lagrange method for double sway pendulum, if you try with Newton method you will most probably arrive at WRONG equation of motion (unless you are a supermind and can predict all possible forces, that easy in spring double pendulum).