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The lagrangian is defined as:

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A Lagrangian function is L=(12x˙2−12ω2x2)e2kt and the basic Noether identity, (3.22.1), becomes (3.22.24)[x˙F˙−ω2xF−f˙(12x˙2+12ω2x2)+fk(x˙2−ω2x2)]e2kt−P˙=0.
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