O Consider the Lagrangian function on R2 (defined by the Cartesian coordinates (x, y)) given by L = - ₁m (x² — y²) + a(y² − x²), - where m and a are constants. (i) Show to first order in € (that is, ignore terms of order €² and higher), that L is invariant u transform (x, y) + (x + ey, y + ex). Find the integral of motion predicted by Noether's theorem for the Lagrangian function
O Consider the Lagrangian function on R2 (defined by the Cartesian coordinates (x, y)) given by L = - ₁m (x² — y²) + a(y² − x²), - where m and a are constants. (i) Show to first order in € (that is, ignore terms of order €² and higher), that L is invariant u transform (x, y) + (x + ey, y + ex). Find the integral of motion predicted by Noether's theorem for the Lagrangian function
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Transcribed Image Text:O Consider the Lagrangian function on R2 (defined by the Cartesian coordinates (x, y)) given by
L =
-
₁m (x² — y²) + a(y² − x²),
-
where m and a are constants.
(i) Show to first order in € (that is, ignore terms of order €² and higher), that L is invariant u
transform
(x, y) + (x + ey, y + ex).
Find the integral of motion predicted by Noether's theorem for the Lagrangian function
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