Lagrangian

In other words, the Lagrangian of a system is not unique.

It is also possible to derive the results from the Lagrangian directly.

The action and Lagrangian both contain the dynamics of the system for all times.

The matter Lagrangian is assumed to be independent of the connection.

Overall, the Lagrangian has units of energy, but no single expression for all physical systems.

In order to construct the most general possible Lagrangian, one must solve this huge system!

This is enough information to write out the Lagrangian.

Each Lagrangian will obtain exactly the same equations of motion.

A particle physics model is essentially described by its Lagrangian.

They can be found around the two Lagrangian points 60 ahead of and behind Mars.

It is constructed from the Lagrangian for the chosen quantum field theory.

The interaction energy is the negative of the interaction Lagrangian.

In some cases, the Lagrangian has properties which can provide information about the system without solving the equations of motion.

Due to its complexity, this Lagrangian is best described by breaking it up into several parts as follows.

The equation of motion for is: and the Lagrangian becomes:

The Lagrangian for this system can be written as:

The equations of motion in physical theories can often be derived from an object called the Lagrangian.

An important property of the Lagrangian is that conserved quantities can easily be read off from it.

The five Lagrangian points are labeled and defined as follows:

Suppose that there is a parameter in the Lagrangian which can be varied, usually a source for a field.

In this case, one says that the Lagrangian exhibits spontaneous symmetry breaking.

The Lagrangian for the gravitational field is spin-2.

The kinetic energy is again the only contribution to the Lagrangian:

For pure wave motion the Lagrangian is expressed in terms of the field and its derivatives.

That is dealt with in the next section by adding yet another term, , to the Lagrangian.