Mathieu transformation

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

:<math>\sum_i p_i \delta q_i=\sum_i P_i \delta Q_i \,</math>

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 <math>q_i</math> and <math>Q_i</math> '''only''' (without any <math>p_i,P_i</math> involved).

:<math> \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} </math>

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

== See also == * Canonical transformation

== References == * {{cite book | author=Lanczos, Cornelius | title=The Variational Principles of Mechanics | location= Toronto | publisher=University of Toronto Press | year=1970 | isbn=0-8020-1743-6}} * {{cite book | author=Whittaker, Edmund | title=A Treatise on the Analytical Dynamics of Particles and Rigid Bodies}}

Category:Mechanics Category:Hamiltonian mechanics