Show that the Lagrangian (L=left(q_{1} dot{q}_{2}-q_{2} dot{q}_{1} ight)^{2}-aleft(q_{1}-q_{2} ight)^{4}) is invariant under the transformations and construct the

Show that the Lagrangian \(L=\left(q_{1} \dot{q}_{2}-q_{2} \dot{q}_{1}\right)^{2}-a\left(q_{1}-q_{2}\right)^{4}\) is invariant under the transformations

and construct the corresponding conserved quantity.

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-8 (2) - (*** 1.) (2) S 1-s