定义3.20(矢量场的李导数(Lie Derivatives of Vector Fields0))。设 X 和 Y 是流形 M 上的光滑矢量场。我们定义 X 沿 Y 的李导数( Lie derivative)为: $$ {\left( {\mathcal{L}}_{X}Y\right) }_{p} \mathrel{\text{:=}} {\left. \frac{d}{dt}\right| }_{t = 0}{\left( {\Phi ...
Definition:(Lie derivative) Given a manifold M , a vector field X , and any type of tensor field T , the Lie derivative of T along X is also a tensor field of the same type, defined by : \mathcal{L}_XT|_p=\lim_{t\rightarrow 0}\frac{(\phi_t^*T)|_p-T|_p}{t} 下面...
calculate the Lie derivative of a vector field, differential form, tensor, or connection with respect to a vector field Calling Sequence Parameters Description Examples Calling Sequence LieDerivative(X, T) Parameters X - a vector field on a manifold M or a vector in a Lie algebra A ...
The Lie derivative of a connectionnabla_Y(Z)is the type(1, 2)tensor fieldS = LieDerivative(X, nabla), defined (when viewed as mapping from pairs of vector fields to vector fields) byS(Y, Z) = LieDerivative(X, nabla_Y(Z)) - nabla_{LieDerivative(X, Y)}(Z) - nabla_X(LieDerivat...
Lie DerivativesThis chapter is devoted to the study of a particularly important construction involving vector fields, called the Lie derivative. This is a method of computing the "directional derivative" of a vector field with respect to another vector field....
The Lie derivative of a differential form is defined in a similar way to the Lie derivative of a vector field, but the chapter uses the pullback instead of the pushforward to compare nearby values. One can rearrange the product formula so that it becomes the global formula for the Lie ...
Lie derivatives take into account the change of a function along the flow of another function, while partial derivatives only measure the change in one direction. Additionally, the Lie derivative of a function along a vector field does not depend on the choice of coordinates, while partial deriva...
Lie derivativeCovariant derivativeTo say that a constitutive model has to verify "the principle of material objectivity" to ensure its frame-indifference has... E Rouhaud,B Panicaud,R Kerner - 《Computational Materials Science》 被引量: 20发表: 2013年 Affine and projective vector fields on spray...
unique section Xc ∈Γ(Lτ E) that projects over X and satisfies ρτ (Xc)θ = LEX θ for all θ∈Γ(E∗), where θ : E −→ R is the linear function defined by the pairing θ(e) = θ(τ ∗(e)), e and LEX := iX ◦ dE + dE ◦ iX is the Lie derivative. ...
为了解决这一问题,我们引入了李导数(Lie Derivative)的概念,使用流动映射 \Phi_t 把一个点的向量场“推进”到另一个点,保证它们位于同一位置,可以进行比较。 李导数的思想是借助流动映射 \Phi_t 将 Y(\gamma(t + \delta)) 推回到 Y(\gamma(t)) 的位置,然后进行相减,以定义向量场的变化。练习...