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Scaling Symmetry and Integrable Spherical Hydrostatics
2013
Journal of Modern Physics
Any symmetry reduces a second-order differential equation to a first integral: variational symmetries of the action (exemplified by central field dynamics) lead to conservation laws, but symmetries of only the equations of motion (exemplified by scale-invariant hydrostatics) yield first-order non-conservation laws between invariants. We obtain these nonconservation laws by extending Noether's Theorem to non-variational symmetries and present an innovative variational formulation of spherical
doi:10.4236/jmp.2013.44069
fatcat:mjuchcdd45dylapu6el5w2cvvi