Mathieu transformation

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).

$\begin{align} \Omega_1(q_1,q_2,\ldots,q_n,Q_1,Q_2,\ldots Q_n) & =0 \\ & {}\ \ \vdots\\ \Omega_m(q_1,q_2,\ldots,q_n,Q_1,Q_2,\ldots Q_n) & =0 \end{align}$

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

See also

• Canonical transformation