Mathieu transformation
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 {\displaystyle \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 {\displaystyle q_{i}} and Q i {\displaystyle Q_{i}} only (without any p i , P i {\displaystyle p_{i},P_{i}} involved).