One of my favorite memories from classical mechanics!anuttarasammyak said:Have you read Feynman's lecture of
https://www.feynmanlectures.caltech.edu/II_19.html happy wheels ?
It might help you.
The Lagrangian is a mathematical function that describes the dynamics of a physical system. It is derived from the principle of least action, which states that the path a system takes between two points in time is the one that minimizes the action (a quantity related to the energy) of the system. The Lagrangian is significant because it allows us to describe and analyze the behavior of complex systems in a concise and elegant manner.
The Euler-Lagrange equation is a differential equation that describes the dynamics of a system in terms of its Lagrangian. It is derived from the principle of least action, which involves taking the derivative of the action with respect to the system's variables and setting it equal to zero. This results in a set of equations that govern the behavior of the system.
The Lagrangian and the Hamiltonian are two different mathematical functions that describe the dynamics of a system. The main difference between them is that the Lagrangian is expressed in terms of the system's position and velocity, while the Hamiltonian is expressed in terms of the system's position and momentum. The Hamiltonian is also related to the total energy of the system, while the Lagrangian is not.
In classical mechanics, the Lagrangian is used to describe the motion of a system in terms of its position and velocity. It allows us to derive the equations of motion for the system and analyze its behavior. The Lagrangian is also used to find conserved quantities, such as energy and momentum, which are important in understanding the behavior of physical systems.
Yes, the Lagrangian can be applied in various fields of science, such as quantum mechanics, electromagnetism, and general relativity. It is a powerful tool for describing the dynamics of complex systems and has applications in many areas of physics and engineering.