Classical Dynamics of Particles and Systems · Problem 1-20

Newtonian Mechanics—Single Particle — Marion & Thornton

Physics — Mechanics · levi-civita-symbol

Problem

Show that ((a))

\displaystyle\sum_{i,j} \varepsilon_{ijk}\,\delta_{ij} = 0

((b))

\displaystyle\sum_{j,k} \varepsilon_{ijk}\,\varepsilon_{ijk} = 2\delta_{il}

((c))

\displaystyle\sum_{i,j,k} \varepsilon_{ijk}\,\varepsilon_{ijk} = 6