“Christoffel symbol”的概念、定义、翻译、参考文献-科学参考

Christoffel symbol

Mathematics

单词	Christoffel symbol
释义	Christoffel symbol Mathematics For a parameterized surface r(u,v) the Christoffel symbols $Γ_{i j}^{k}$ are defined by $r_{u u} = Γ_{11}^{1} r_{u} + Γ_{11}^{2} r_{v} + L n,$ $r_{u v} = Γ_{12}^{1} r_{u} + Γ_{12}^{2} r_{v} + M n,$ $r_{v v} = Γ_{22}^{1} r_{u} + Γ_{22}^{2} r_{v} + N n,$ where n denotes a unit normal and L,M,N are the coefficients of the second fundamental form. The Christoffel symbols are intrinsic (and so may be expressed in terms of the first fundamental form), and a curve r(u(s),v(s)) is a geodesic parametrized by arc length s if $\ddot{u} + Γ_{11}^{1} {\dot{u}}^{2} + 2 Γ_{12}^{1} \dot{u} \dot{v} + Γ_{22}^{1} {\dot{v}}^{2} = 0,$ $\ddot{v} + Γ_{11}^{2} {\dot{u}}^{2} + 2 Γ_{12}^{2} \dot{u} \dot{v} + Γ_{22}^{2} {\dot{v}}^{2} = 0.$
随便看	methyl ethanoate methyl ethyl ketone methyl group methylidyne methyl methacrylate methylome methyl orange methylphenols methyl red methyl violet methylxanthines Metis Metius, Jacobus metocean data metol Meton Metonic cycle MetOp MetOp-SG metre metre bridge metre(symbol: m) metric metric space metric system