Find the infinitesimals corresponding to the one-parameter rotation group (rotations in the plane), and the first, second, and third prolongations of eta.
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These prolongations of eta enter the expression of the extended related infinitesimal generator (a differential operator, see infgen).
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| (9) |
You can also determine point symmetries for second order ODEs. The general case is as follows:
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| (10) |
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| (11) |
The prolongation of order 0 is just eta(x,y):
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The first and second prolongations of eta look like this:
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| (13) |
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| (14) |
Finally, here is the general case of a dynamical symmetry in the framework of second order ODEs and the first prolongation of eta.
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| (15) |
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| (16) |