Recent zbMATH articles in MSC 70H14https://www.zbmath.org/atom/cc/70H142021-03-30T15:24:00+00:00WerkzeugOn periodic solutions to Lagrangian system with singularities and constraints.https://www.zbmath.org/1455.370512021-03-30T15:24:00+00:00"Zubelevich, O."https://www.zbmath.org/authors/?q=ai:zubelevich.oleg-eduardovichA time-dependent mechanical Lagrangian with gyroscopic forces and ideal constraints is considered. It is shown that, provided certain inequalities are satisfied, the Euler-Lagrange equations admit non-trivial \(\omega\)-periodic (arithmetic quasi-periodic) solutions which are odd as functions of time. The author considers in detail the example of a tube rotating freely in a vertical plane with a small ball rolling in it and of a point moving in a plane under the potential \(V=-\gamma \left( |{r}-{r}_0|^{-d}+|{r}+{r}_0|^{-d} \right)\), where \(\gamma \in \mathbb R^+\) and \({r}_0\neq 0\) is a fixed vector.
Reviewer: Giovanni Rastelli (Vercelli)Basic bifurcation scenarios in neighborhoods of boundaries of stability regions of libration points in the three-body problem.https://www.zbmath.org/1455.700072021-03-30T15:24:00+00:00"Yumagulov, M. G."https://www.zbmath.org/authors/?q=ai:yumagulov.marat-gayazovichSummary: In this paper, we construct stability regions (in the linear approximation) of triangular libration points for the planar, restricted, elliptic three-body problem and examine bifurcations that occur when parameters of the system pass through the boundaries of these regions. A new scheme for the construction of stability regions is presented, which leads to approximation formulas describing these boundaries. We prove that on one part of the boundary, the main scenario of bifurcation is the appearance of nonstationary \(4 \pi \)-periodic solutions that are close to a triangular libration point, whereas on the other part, the main scenario is the appearance of quasiperiodic solutions.Book review of: A. J. Hahn, Basic calculus of planetary orbits and interplanetary flight. The missions of the Voyagers, Cassini, and Juno.https://www.zbmath.org/1455.000222021-03-30T15:24:00+00:00"Schulz, Volker H."https://www.zbmath.org/authors/?q=ai:schulz.volker-hReview of [Zbl 1444.85001].