Chaplygin's equation

Chaplygin's equation

In mathematics, Chaplygin's equation, named after Sergei Alekseevich Chaplygin, is a partial differential equation useful in the study of transonic flow.[1] It is


\Psi_{\theta\theta}+
\frac{v^2}{1-\frac{v^2}{c^2}}\Psi_{vv}+v\Psi_v=0.

Here, c = c(v) is the speed of sound, determined by the equation of state of the fluid and Bernoulli's principle.

References

  1. ^ Landau, L. D.; Lifshitz, E. M. (1982). Fluid Mechanics (2 ed.). Pergamon Press. p. 432. 

Wikimedia Foundation. 2010.

Игры ⚽ Нужна курсовая?

Look at other dictionaries:

  • Chaplygin — (masculine) or Chaplygina (feminine; also masculine genitive) may refer to: Aleksey Pavlovich Chaplygin, russian writer Sergey Chaplygin (1869–1942), Russian Soviet physicist Chaplygin (crater), a lunar crater named after him Chaplygin, Lipetsk… …   Wikipedia

  • Chaplygin gas — [1] ,[2] which occurs in certain theories of cosmology, is a hypothetical substance that satisfies an exotic equation of state in the form p = − A / ρα where p is the pressure, ρ is the density, with α = 1 and A a positive constant. The substance …   Wikipedia

  • Sergey Chaplygin — Sergey Alexeyevich Chaplygin ( ru. Сергей Алексеевич Чаплыгин; April 5, 1869 ndash;October 8, 1942) was a Russian physicist, mathematician, and mechanical engineer. He is known for mathematical formulas such as Chaplygin s equation. He graduated… …   Wikipedia

  • Euler-Tricomi equation — In mathematics, the Euler Tricomi equation is a linear partial differential equation useful in the study of transonic flow. It is named for Leonhard Euler and Francesco Giacomo Tricomi.: displaystyleu {xx}=xu {yy}.It is hyperbolic in the half… …   Wikipedia

  • List of Russian mathematicians — Andrey Kolmogorov, a preeminent 20th century mathematician. This list of Russian mathematicians includes the famous mathematicians from the Russian Empire, the Soviet Union and the Russian Federation. This list is incomplete; you can help by …   Wikipedia

  • List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia

  • List of Russian people — The Millennium of Russia monument in Veliky Novgorod, featuring the statues and reliefs of the most celebrated people in the first 1000 years of Russian history …   Wikipedia

  • Energie sombre — Énergie sombre  Ne doit pas être confondu avec matière sombre ou Trou noir. En cosmologie, l énergie sombre, ou énergie noire (dark energy en anglais) est une forme d énergie inconnue en laboratoire emplissant tout l Univers et dotée d une… …   Wikipédia en Français

  • Énergie noire — Énergie sombre  Ne doit pas être confondu avec matière sombre ou Trou noir. En cosmologie, l énergie sombre, ou énergie noire (dark energy en anglais) est une forme d énergie inconnue en laboratoire emplissant tout l Univers et dotée d une… …   Wikipédia en Français

  • Énergie sombre —  Ne doit pas être confondu avec matière sombre ni Trou noir. En cosmologie, l énergie sombre, ou énergie noire (dark energy en anglais) est une forme d énergie inconnue en laboratoire emplissant tout l Univers et dotée d une pression… …   Wikipédia en Français

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”