(b) Consider the Lagrangian function on R² (defined by the Cartesian coordinates (x, y)) given by 1 L = - ¡m (x² − ÿ²) + 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 under the transform (x, y)(x+ey, y + ex).
(b) Consider the Lagrangian function on R² (defined by the Cartesian coordinates (x, y)) given by 1 L = - ¡m (x² − ÿ²) + 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 under the transform (x, y)(x+ey, y + ex).
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Transcribed Image Text:(b) Consider the Lagrangian function on R² (defined by the Cartesian coordinates (x, y)) given by
1
L
=
-
¡m (x² − ÿ²) + 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 under the
transform
(x, y)(x+ey, y + ex).
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