Unformatted text preview: ( b j e j ) = a i b j e i × e j = a i b j ε ijk e k (3) Remarks: The Kronecker delta can be used as identity matrix: I ˆ= δ ij (4) The permutation has the properties that, ε ijk = ε jki = ε kij (5) and, ε ijk =-ε jik . (6) There is exists the following relation between the permutation and the Kronecker delta, 1. ε ijk ε pqk = δ ip δ jq-δ iq δ jp (7) Here i,j,p,q are free indices and must match on both sides of the equation. k is a dummy index. 2. ε ijk ε pjk = 2 δ ip (8) Here i,p are free indices and must match on both sides of the equation. j,k are dummy indices. 3. ε ijk ε ijk = 6 (9) 1...
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- Spring '10
- Mechanical Engineering, Identity matrix, Levi-Civita symbol, Mechanical Systems Center of Mechanics ETH Zurich Department of Mechanical and Process Engineering