Poincaré-Cartan integral invariants of nonconservative dynamical systems (Q1805636)

In this paper the authors review some results on the Poincaré and Poincaré-Cartan integral invariants from the traditional point of view and discuss the adjoint symmetries of a system of \(n\) second-order ordinary differential equations. For weak nonconservative systems the authors prove that a system of dynamical equations and their adjoint equations are canonical in an extended phase space and there exist integral invariants in the space. Integral invariants for pseudoconservative systems are constructed. The one-dimensional damped vibration is reanalyzed. It is shown that the Poincaré and Poincaré-Cartan integral invariants exist in the extended phase space.