Generalized submersiveness of second-order ordinary differential equations

We generalize the notion of submersive second-order differential equations by relaxing the condition that the decoupling stems from the tangent lift of a basic distribution. It is shown that this leads to adapted coordinates in which a number of first-order equations decouple from the remaining second-order ones

Second-order dynamical systems of Lagrangian type with dissipation

We give a coordinate-independent version of the smallest set of necessary and sufficient conditions for a given system of second-order ordinary differential equations to be of Lagrangian form with additional dissipative forces

Addendum to: The integrability conditions in the inverse problem of the calculus of variations for second-order ordinary differential equations

An omission in the outline of the general approach to the inverse problem in Acta Appl. Math. (54 (1998), pp. 233–273) is clarified

Autonomous three dimensional Newtonian systems which admit Lie and Noether point symmetries

We determine the autonomous three dimensional Newtonian systems which admit Lie point symmetries and the three dimensional autonomous Newtonian Hamiltonian systems, which admit Noether point symmetries. We apply the results in order to determine the two dimensional Hamiltonian dynamical systems which move in a space of constant non-vanishing curvature and are integrable via Noether point symmetries. The derivation of the results is geometric and can be extended naturally to higher dimensions.Comment: Accepted for publication in Journal of Physics A: Math. and Theor.,13 page