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Correction to: Generalization of Hamiltonian mechanics to a three-dimensional phase space.

Authors :
Sato, Naoki
Source :
Progress of Theoretical & Experimental Physics: PTEP; Apr2024, Vol. 2024 Issue 4, p1-6, 6p
Publication Year :
2024

Abstract

In a recent paper [N. Sato, Prog. Theor. Exp. Phys. 2021, 6, 063A01 (2021)] we introduced a generalization of Hamiltonian mechanics to three-dimensional phase spaces in terms of closed 3-forms. This correction addresses an error in the proof of theorem 3, which concerns the existence of a coordinate change transforming a closed 3-form into a constant form. Indeed, invertibility of a 3-form is not sufficient to ensure the existence of a solution X<subscript>t</subscript> to eq. (77) when n > 3. The theorem can be corrected by restricting the class of 3-forms to those that are relevant to generalized Hamiltonian mechanics. Although the new theorem requires a stronger hypothesis, the formulation of dynamical systems with 2 invariants in terms of closed 3-forms, which is the key contribution of the paper, holds. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
20503911
Volume :
2024
Issue :
4
Database :
Complementary Index
Journal :
Progress of Theoretical & Experimental Physics: PTEP
Publication Type :
Academic Journal
Accession number :
177084169
Full Text :
https://doi.org/10.1093/ptep/ptae036