Non‐Leibniz Hamiltonian and Lagrangian formalisms for certain class of dissipative systems. Issue 3 (23rd April 2019)

• Record Type: Journal Article
• Authors: Kobelev, Vladimir
• Is Part Of: Computational and mathematical methods. Volume 1:Issue 3(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-04-23
• Subjects: blue and red shift -- dissipative hamiltonian system -- generalized Leibniz rule; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1035
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract : 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 operator ( κ ‐operator) with a nonzero 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 generalized differentiation operator reduces to the common differentiation operator. The κ ‐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 closed form.