TOPICS
Search

Lagrange's Equation

The partial differential equation

(1+f_y^2)f_(xx)-2f_xf_yf_(xy)+(1+f_x^2)f_(yy)=0

(Gray 1997, p. 399), whose solutions are called minimal surfaces. This corresponds to the mean curvature H equalling 0 over the surface.

d'Alembert's equation

y=xf(y^')+g(y^')

is sometimes also known as Lagrange's equation (Zwillinger 1997, pp. 120 and 265-268).

See also

d'Alembert's Equation, Mean Curvature, Minimal Surface

Explore with Wolfram|Alpha

References

do Carmo, M. P. "Minimal Surfaces." §3.5 in Mathematical Models from the Collections of Universities and Museums (Ed. G. Fischer). Braunschweig, Germany: Vieweg, pp. 41-43, 1986.Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 1997.Zwillinger, D. "Lagrange's Equation." §II.A.69 in Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, pp. 120 and 265-268, 1997.

Referenced on Wolfram|Alpha

Lagrange's Equation

Cite this as:

Weisstein, Eric W. "Lagrange's Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LagrangesEquation.html

Subject classifications