On motions with bursting characters for Lagrangian mechanical systems with a scalar control. I: Existence of a wide class of Lagrangian systems capable of motions with bursting characters
The authors report results of papers of theirs which are concerned with mechanical systems with a scalar control parameter. The so-called semi- Hamiltonian equation \(\dot z=F\bigl[t,u(t),z,\dot u(t)\bigr]\) governs the dynamics of the system, where \(z=(q,p)\) are the generalised coordinates and moments and \(u(t)\) is the control parameter, which can have discontinuities (hyper-impulsive motions). The reported theorems state conditions for \(F\) (with respect to the dependence of \(\dot u(t))\) and the corresponding kinetic energy whether the solutions have (no) bursting character and how the solutions depend on the discontinuities.
scientific article; zbMATH DE number 61700