Block-Separation of Variables: a Form of Partial Separation for Natural Hamiltonians
| Autor: | Claudia Maria Chanu, Giovanni Rastelli |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
0209 industrial biotechnology
Pure mathematics Separation of variables Block (permutation group theory) FOS: Physical sciences Inverse Scalar potential Dynamical Systems (math.DS) 02 engineering and technology 01 natural sciences Set (abstract data type) Matrix (mathematics) 020901 industrial engineering & automation Stäckel systems FOS: Mathematics Partial separation of variables Position-dependent time parametrisation 0101 mathematics Invariant (mathematics) Twist Mathematics - Dynamical Systems Mathematical Physics Mathematics 010102 general mathematics Mathematical Physics (math-ph) Geometry and Topology Analysis |
| Popis: | 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-St\"ackel 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 St\"ackel separation of variables. We classify the block-separable coordinates of $\mathbb E^3$. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|