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