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Mechanics with non‐Leibniz derivatives
Author(s) -
Kobelev Vladimir
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800002
Subject(s) - dissipative system , dissipative operator , formalism (music) , hamiltonian (control theory) , lagrangian , operator (biology) , hamiltonian formalism , mathematics , mathematical physics , scaling , covariant hamiltonian field theory , ladder operator , classical mechanics , hamiltonian system , physics , compact operator , quantum mechanics , computer science , geometry , mathematical optimization , art , repressor , covariant transformation , chemistry , visual arts , musical , biochemistry , transcription factor , gene , programming language , extension (predicate logic)
The non‐Leibniz Hamiltonian and Lagrangian formalism for the certain class of dissipative systems is introduced in this article. The formalism is based on the generalized differentiation κ‐operator with a non‐zero Leibniz defect. The Leibniz defect of the introduced operator linearly depends on one scaling parameter. In a special case, if the Leibniz defect vanishes, the κ‐operator reduces to the common differentiation operator. The new operator allows the formulation of the variational principles and corresponding equations of Lagrange and Hamiltonian types for dissipative systems. The solutions of some generalized dynamical equations are provided in closed form.