正本清源一一般曲线坐标系下场论恒等式推导 Euclid空间中场论恒等式的推导 1Rc9理:、Q (e“(x)g,88,8(x)=Ve“(x)g③g,③g4(x)=0 G (x)=(g1(x)g8g(x)=V8(x)g'⑧g(x) k 3 euclid空间基本性质:V=VV 摘自20110学年第一学期试卷 Problem 1(Field Analysis- Identifies of Tensor Fields) To prove the following iden tities of the tensor fields in the point of view of general curvilinear coordinates 1. For any vector field b(a)in Rs, the following identity is keeping valid: ×V×b=V(Vb)-△②b∈R g. For any symmetric affine tensor重∈少2(R3) such that重=, the following identity is keeping valid: V×(V×重)*=V⑧(V)+(V·)⑧V-V2重-VVtr()-IⅣ更.V-V2tr(正本清源 —— 一般曲线坐标系下场论恒等式推导                 0 1.Ricci 0 2. 3. ijk ijk l l i jk l i jk ij ij l l ij l ij ijk j k k j ipq p q p q pq q p x xg g g x xg g g x x x G x g xg g x g xg g x x x Euclid                                      ——Euclid空间中场论恒等式的推 引理： 空间基 质 导 本性 ： 摘自 2011－2012学年第一学期试卷