Applied Mathematics/Lagrange Equations

Lagrange Equation edit


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




Hence the Lagrangian   is


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


In the same way, we have