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| The '''Mathieu transformations''' make up a subgroup of [[canonical transformation]]s preserving the [[differential form]]
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| :<math>\sum_i p_i \delta q_i=\sum_i P_i \delta Q_i \,</math>
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| The transformation is named after the French mathematician [[Émile Léonard Mathieu]].
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| == Details ==
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| In order to have this [[Invariant (mathematics)|invariance]], there should exist at least one [[relation (mathematics)|relation]] between <math>q_i</math> and <math>Q_i</math> '''only''' (without any <math>p_i,P_i</math> involved).
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| :<math>
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| \begin{align}
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| \Omega_1(q_1,q_2,\ldots,q_n,Q_1,Q_2,\ldots Q_n)=0\\
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| \ldots\\
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| \Omega_m(q_1,q_2,\ldots,q_n,Q_1,Q_2,\ldots Q_n)=0
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| \end{align}
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| </math>
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| where <math>1 < m \le n</math>. When <math>m=n</math> a Mathieu transformation becomes a [[Lagrange point transformation]].
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| == See also ==
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| * [[Canonical transformation]]
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| == References ==
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| * {{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}}
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| * {{cite book | author=[[Edmund Whittaker|Whittaker]], Edmund | title=A Treatise on the Analytical Dynamics of Particles and Rigid Bodies }}
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| [[Category:Mechanics]]
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| [[Category:Hamiltonian mechanics]]
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| {{classicalmechanics-stub}}
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Hello! Let me start by stating my name - Ron Stephenson. I am a cashier and I'll be promoted quickly. Delaware is the only location I've been residing in. One of his favorite hobbies is taking part in crochet but he hasn't produced a dime with it.
Take a look at my website - www.Mystic-Balls.com