# Block-Separation of Variables: a Form of Partial Separation for Natural Hamiltonians

@article{Chanu2018BlockSeparationOV, title={Block-Separation of Variables: a Form of Partial Separation for Natural Hamiltonians}, author={Claudia M. Chanu and Giovanni Rastelli}, journal={Symmetry, Integrability and Geometry: Methods and Applications}, year={2018} }

We study twisted products $H=\alpha^rH_r$ of natural autonomous Hamiltonians $H_r$, each one depending on a separate set, called here separate $r$-block, of variables. We show that, when the twist functions $\alpha^r$ are a row of the inverse of a block-Stackel matrix, the dynamics of $H$ reduces to the dynamics of the $H_r$, modified by a scalar potential depending only on variables of the corresponding $r$-block. It is a kind of partial separation of variables. We characterize this block…

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