Application of the modified Euler-Lagrange equation to multi-degree-of-freedom problems

DOI: https://doi.org/10.55228/JTST.14(1).11-20

Keywords

Classical mechanics, Engineering mechanics, Multi-degree-of-freedom systems, Euler-Lagrange equation

Abstract

In mechanical engineering, systems are often composed of multiple interconnected bodies, leading to complex motions and multiple degrees of freedom. These systems, influenced by various external forces, are challenging to solve, especially when the forces include both conservative and non-conservative elements. Traditional methods, such as the Euler-Lagrange equation and the Lagrange equations of the second kind, are commonly used to derive differential equations for these systems. However, these approaches can be inadequate for systems with intricate motions and mixed types of external forces. To address these limitations, the modified Euler-Lagrange equation offers an effective alternative. This paper presents the theoretical framework of the modified Euler-Lagrange equation and illustrates its application through two detailed examples of multi-degree-of-freedom systems in classical mechanics. Although the paper does not include an in-depth evaluation of the method’s effectiveness, it offers a comprehensive approach that simplifies the process of solving a variety of dynamic problems.

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