Weyl's lemma (Laplace equation)

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

$\sum _{i}p_{i}\delta q_{i}=\sum _{i}P_{i}\delta Q_{i}\,$

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).

${\begin{aligned}\Omega _{1}(q_{1},q_{2},\ldots ,q_{n},Q_{1},Q_{2},\ldots Q_{n})=0\\\ldots \\\Omega _{m}(q_{1},q_{2},\ldots ,q_{n},Q_{1},Q_{2},\ldots Q_{n})=0\end{aligned}}$

where $1<m\leq n$. When $m=n$ a Mathieu transformation becomes a Lagrange point transformation.

See also

• Canonical transformation

References

• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
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• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

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