In this case, introduce the Lagrangian, L = T − V, so these equations of motion become d d t ∂ ∂ L ∂ ∂ q ˙ ˙ j − − ∂ ∂ L ∂ ∂ q j = 0 j = 1 , … … , m . These are known as the Euler-Lagrange equations for a system with m degrees of freedom, or Lagrange's equations of the second kind.