Energy principle and variational method note 17: generalized variational principle (identification factor method)

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$$\begin{gathered} The\; right\; side\; of\; the\; figure\; below\; is\; right“sign\; out”The\; explanation\; of\; ,\; And\; for\; the\; problemmin(x^2+y^2)Satisfyx=2y, \\ Because\; the\; calculation\; error\; is\; too\; large,Exit\; and\; bring\; in,Use\; Lagrange\; multiplier\; method\; , \\ Then\; use\; the\; method\; of\; identifying\; factors,Let\; first-order\; differential=0,\; Identify\lambda \end{gathered}$$

$$The\; first-order\; differential\; corresponds\; to\; the\; first-order\; variational$$

$$After\; introducing\; the\; identification\; factor,\; we\; can\; get\; the\; functional\; without\; Lagrange\; multiplier$$

$$summary$$

$$verification$$

$$Solve\; the\; previous\; approximation\; problem$$

$$Generalized\; variational\; principle$$