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Conference Proceedings
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4th International Conference on Physics and Control (PhysCon 2009)
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Asymptotical Symmetrization of Hamilton Systems
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We discuss a new algorithms of calculations of Hamiltonian normal form. A normal form of a Hamilton system has two main properties: a) Tailor expansion of the normal form has the simplest form; b) its linear part commutates with a nonlinear one. Property a is used for the normalization procedure. Property b) is used to build asymptotic solutions. For this purpose, instead of the normal form we define symmetrical form: a form satisfying property b). Symmetrization algorithm is reduced to sequential calculations of the quadrature in the approximation of each order and is essentially simpler than all the classical normalization procedures.