sentences:  The action of the path "u", denoted "S"("u"), is given by
  where "L" is a function of time, position and velocity known as the Lagrangian.The principle of least action states that, given an initial state "x"0 and a final state "x"1 in R"n", the trajectory that the system determined by "L" will actually follow must be a minimizer of the action functional "S" satisfying the boundary conditions "u"(0) = "x"0, "u"(T) = "x"1.Furthermore, the critical points (and hence minimizers) of "S" must satisfy the Euler–Lagrange equations for "S"