• DOI:10.3842/SIGMA.2019.013
• Corpus ID: 85523499

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}
}

• C. Chanu, G. Rastelli
• Published 6 August 2018
• Mathematics
• Symmetry, Integrability and Geometry: Methods and Applications

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-separation in an invariant way by writing in block-form classical results of Stackel separation of variables. We classify the block-separable coordinates of $\mathbb E^3$.