Lagrangian models are a type of mathematical model used in physics and engineering to describe the motion of particles or systems. These models are based on the Lagrangian formalism, which is a mathematical framework that uses the concept of action to derive equations of motion for a system. In Lagrangian models, the motion of particles or systems is described in terms of generalized coordinates and generalized velocities. The Lagrangian function, which is a function of these variables, is used to derive the equations of motion using the principle of least action. Lagrangian models are commonly used in classical mechanics, fluid dynamics, and quantum mechanics to study the behavior of complex systems. They are particularly useful for systems with constraints or varying degrees of freedom. Overall, Lagrangian models provide a powerful tool for analyzing and predicting the behavior of physical systems, making them a valuable research area in applied mathematics and physics.