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This article is cited in 3 scientific papers (total in 3 papers)
Block-Separation of Variables: a Form of Partial Separation for Natural Hamiltonians
Claudia Maria Chanu, Giovanni Rastelli Dipartimento di Matematica, Università di Torino, Torino, via Carlo Alberto 10, Italy
Abstract:
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-Stäckel 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 Stäckel separation of variables. We classify the block-separable coordinates of $\mathbb E^3$.
Keywords:
Stäckel systems; partial separation of variables; position-dependent time parametrisation.
Received: August 7, 2018; in final form February 14, 2019; Published online February 23, 2019
Citation:
Claudia Maria Chanu, Giovanni Rastelli, “Block-Separation of Variables: a Form of Partial Separation for Natural Hamiltonians”, SIGMA, 15 (2019), 013, 22 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1449 https://www.mathnet.ru/eng/sigma/v15/p13
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Abstract page: | 163 | Full-text PDF : | 42 | References: | 21 |
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