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Line 78:
\beta^2\partial_m\partial_mu_i=-f_i/\rho</math>
Taking the [[divergence]] of both sides of this static equation and assuming a [[conservative force]], (<math>\partial_i f_i=0</math>) we have
:<math>\partial_i A_{ij}u_j = (\alpha^2-\beta^2)\partial_i\partial_i\partial_ju_j+\beta^2\partial_i\partial_m\partial_mu_i = 0</math>
Line 90:
:<math>\partial_i\partial_i\partial_ju_j = 0</math>
Taking the [[Laplacian]] of both sides of the static equation, a conservative force will give <math>\partial_k\partial_kf_i=0</math> and we have
:<math>\partial_k\partial_kA_{ij}u_j = (\alpha^2-\beta^2)\partial_k\partial_k\partial_i\partial_ju_j+\beta^2\partial_k\partial_k\partial_m\partial_mu_i=0</math>
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