Comparison of the modelling techniques of dynamical systems using momentum and energy principles

Abstract

In undergraduate courses such as engineering mechanics and modelling and simulation, students mostly use Newton’s second law to derive equations of motion in dynamics problems. However, it might be easier and faster in some dynamics problems to use Lagrange’s equation instead of Newton’s second law.  To analyze the reason of this situation we will compare the general features of each type of these methods from different aspects. Then we will apply both to some examples and indicate the differences and levels of difficulty accompanying the application of each technique. Three examples from mechanical systems and one example from electrical systems are presented here to show the basic differences between Newton’s second law of motion and Lagrange’s equation. Three examples include a system with a single degree of freedom (translational), two degrees of freedom and multiple degrees of freedom in translation and rotation. For electrical systems, a two degrees of freedom circuit with dual portions is explained using Lagrange’s equation and Kirchhoff law. The advantages and disadvantages of each approach and how the principal concepts in system dynamics are explained to the students are also highlighted.