Mathieu transformation

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

∑ piδqi = ∑ PiδQi
i i

The transformation is named after the French mathematician Émile Léonard Mathieu.

[edit] Details

In order to have this invariance, there should exist at least one relation between qi and Qi only (without any pi,Pi involved).

\begin{align} \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{align}

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

[edit] See also

[edit] References

  • Lanczos, Cornelius (1970). The Variational Principles of Mechanics. Toronto: University of Toronto Press. ISBN 0-8020-1743-6. 
  • Whittaker, Edmund. A Treatise on the Analytical Dynamics of Particles and Rigid Bodies. 
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