Prikl. Mat. Mekh., 2012, Volume 76, Issue 4, Pages 526–539
nvariant manifolds of Hamilton's equations
V. V. Kozlov
The invariance conditions of smooth manifolds of Hamilton's equations are represented in the form of multidimensional Lamb's equations from the dynamics of an ideal fluid. In the stationary case these conditions do not depend on the method used to parameterize the invariant manifold. One consequence of Lamb's equations is an equation of a vortex, which is invariant to replacements of the time-dependent variables. A proof of the periodicity conditions of solutions of autonomous Hamilton's equations with $n$ degrees of freedom and compact energy manifolds that admit of $2n-3$ additional first integrals is given as an application of the theory developed.
Journal of Applied Mathematics and Mechanics, 2012, 76:4, 378–387
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