This paper is devoted to geometric formulation of the regular (resp. strongly regular) Hamiltonian system. The notion of the regularization of the second order Lagrangians is presented. The regularization procedure is applied to concrete example.
The aim of the paper is to announce some recent results concerning Hamiltonian theory. The case of second order Euler–Lagrange form non-affine in the second derivatives is studied. Its related second order Hamiltonian systems and geometrical correspondence between solutions of Hamilton and Euler–Lagrange equations are found.
Understanding the concept of infinity, which is one of the fundamental concepts of mathematics, assumes significant degree of cognitive maturity of every individual. For this reason this concept is a source of many obstacles and difficulties in a teaching process. Students meet for the first time with the notion of infinity in an explicit form in connection with the concept of convergence of sequences and series. As confirmed by several studies, many practicing teachers or our own experience, the...
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