This document is a brief overview of the Hamilton-Jacobi theory of Chaplygin systems based on [1]. In this paper, after reducing Chaplygin systems, Ohsawa et al. use a technique that they call Chaplygin Hamiltonization to turn the reduced Chaplygin systems into Hamiltonian systems. This method was first introduced in a paper by Chaplygin in 1911 where he reduced some nonholonomic systems by the...

We propose in this paper a new model for describing the unification of dark energy and dark matter. This new model is a further generalization of the generalized Chaplygin gas (GCG) model, thus dubbed new generalized Chaplygin gas (NGCG) model. The equation of state of the NGCG is given by p = −Ã(a)/ρα, where a is the scale factor and Ã(a) = −wXAa −3(1+wX)(1+α). We show that the NGCG model is t...

We propose in this paper a new model for describing the unification of dark energy and dark matter. This new model is a further generalization of the generalized Chaplygin gas (GCG) model, thus dubbed new generalized Chaplygin gas (NGCG) model. The equation of state of the NGCG is given by p = −Ã(a)/ρα, where a is the scale factor and Ã(a) = −wXAa −3(1+wX)(1+α). We show that the NGCG model is t...

The postulation of dark energy and dark matter on the basis of observational results does not end the mystery of their existence. Theoretically new insights into dark matter have been achieved analysing recent experimental data from the cosmic -ray physics. It has been shown that, if the dark matter is a hidden scalar field, then it is not only possible to explain the ATIC / PPB-BETS excess but...