Weyl's lemma (Laplace equation)

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

\sum_{i} p_{i} δ q_{i} = \sum_{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).

\begin{aligned} Ω_{1} (q_{1}, q_{2}, \dots, q_{n}, Q_{1}, Q_{2}, \dots Q_{n}) = 0 \\ \dots \\ Ω_{m} (q_{1}, q_{2}, \dots, q_{n}, Q_{1}, Q_{2}, \dots Q_{n}) = 0 \end{aligned}

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

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