Lagrangian mechanics is a formulation of classical mechanics that is based on the principle of stationary action and in which energies are used to describe motion.

    Lagrange mechanics is based on two basic concepts. The first is the function, which is a function that describes the state of particle motion through kinetic energy and potential energy. Another important quantity is called action, which is used to define the path through time and space. The important thing about the action is that it must be static to get the correct equation of motion. This is called the principle of stationary action, and it is one of the most basic principles that run through all physics.

    Lagrange mechanics uses Kinetic energy and potential energy to find the equation of motion.

The formula for the Lagrangian energy

    The lagrangian formula uses the letter 'L' to define a function of the kinetic and potential energies. T is used to denote kinetic energy, while U is the potential energy (we can use 'V' as well).

    In Lagrangian mechanics, 'L'  is NOT the total energy of an object. It has very little to do with the total energy, which can be stated as a motion of any particular point in time, that is described by the kinetic and potential energy. Potential energy doesn't really describe the motion of an object by itself. It can be amended into other forms of energy (like Kinetic energy in this case).

The lagrangian formula

If we plug the Lagrangian (L= T-U) into the equation, we get:

    This method will help us to find the Lagrangian equation to determine each of energy in the system, thus we can solve and find the velocity (whether it's angular(ω) or radial velocity(v)) at a certain problem.