Mathieu transformation - Alchetron, The Free Social Encyclopedia

The Mathieu transformations make up a subgroup of canonical transformations preserving the differential form

∑ i p i δ q i = ∑ i P i δ Q i

The transformation is named after the French mathematician Émile Léonard Mathieu.

Details

In order to have this invariance, there should exist at least one relation between q i and Q i only (without any p i , P i involved).

Ω 1 ( q 1 , q 2 , … , q n , Q 1 , Q 2 , … Q n ) = 0 ⋮ Ω m ( q 1 , q 2 , … , q n , Q 1 , Q 2 , … Q n ) = 0

where 1 < m ≤ n . When m = n a Mathieu transformation becomes a Lagrange point transformation.

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