Define the linear operator

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.

Reference no: EM132439876

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