# Applied Mathematics/Lagrange Equations

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## Lagrange Equation[edit]

where

The equation above is called **Lagrange Equation**.

Let the kinetic energy of the point mass be and the potential energy be .

is called **Lagrangian**. Then the kinetic energy is expressed by

Thus

Hence the Lagrangian is

Therefore relies on only and . relies on only and . Thus

In the same way, we have