We consider the symplectic Euler method for Hamiltonian systems with holonomic constraints and its generalizations to a class of overdetermined differential-algebraic equations (ODAEs) which are nonlinear in the algebraic variables. It is shown that a straightforward generalization of the symplectic Euler method is inconsistent. A different non-trivial generalization of the symplectic Euler met...

Calogero-Moser systems, which were originally discovered by specialists in integrable systems, are currently at the crossroads of many areas of mathematics and within the scope of interests of many mathematicians. More specifically, these systems and their generalizations turned out to have intrinsic connections with such fields as algebraic geometry (Hilbert schemes of surfaces), representatio...

It is shown that there is a non-Hamiltonian vector field that provides a Lie algebraic connection between Hamiltonian and Lagrangian optics. With the aid of this connection, geometrical optics can be formulated in such a way that all aberrations are attributed to ray transformations occurring only at lens surfaces. That is, in this formulation there are no aberrations arising from simple transi...

We discuss different cases of dissipative Hamiltonian differential-algebraic equations and the linear algebraic systems that arise in their linearization or discretization. For each case we give examples from practical applications. An important feature is (non-Hermitian) system matrix has a positive definite semidefinite Hermitian part. In can solve iteratively by Krylov subspace methods based...

‎In this paper Lie point symmetries‎, ‎Hamiltonian equations and conservation‎ ‎laws of general three-dimensional anisotropic non-linear sourceless heat transfer‎ ‎equation are investigated‎. ‎First of all Lie symmetries are obtained by using the general method‎ based on invariance condition of a system of differential equations under a pro‎longed vector field‎. ‎Then the structure of symmetry ...

Abstract Different representations of linear dissipative Hamiltonian and port-Hamiltonian differential–algebraic equations (DAE) systems are presented compared. Using global geometric algebraic points view, translations between different presented. Characterizations also derived when a general DAE system can be transformed into one these structured representations. Approaches for computing the ...