Infinite Limits

Lagrangian mechanics is a powerful mathematical framework that provides a systematic and elegant approach to understanding the dynamics of physical systems. Developed by Joseph-Louis Lagrange in the late 18th century, it offers an alternative formulation to Newton's laws of motion, providing deeper insights into the fundamental principles governing the behaviour of objects. In this post, we will embark on a comprehensive journey into the realm of Lagrangian mechanics, covering its principles, applications, and significance in the field of physics. Joseph Louis Lagrange Image Credit: Encyclopaedia Britannica The Lagrangian Formulation: At the heart of Lagrangian mechanics lies the concept of the Lagrangian, denoted by L. The Lagrangian is a mathematical function that encapsulates the kinetic and potential energies of a system (KE-PE), providing a comprehensive description of its dynamics. By defining the Lagrangian, we can derive the equations of motion for a system using the princi...