Reference no: EM132439876
Question - Let ψ ≡ (ξ, η1, η2, ξ', η'1, η'2) denote a normal mode for the particle displacements. Define the linear operator
L^y(ψ) ≡ (ξ', η'1, η'2, ξ, η1, η2)
≡ switching coordinates using y-axis as a symmetry axis.
Similarly, we define
L^x(ψ) ≡ (ξ, η2, η1, ξ', η'2, η'1)
≡ switching coordinates using x-axis as a symmetry axis.
Clearly, both L^x(ψ) and L^y(ψ) are still normal modes of the same frequency.