Radial stability of periodic orbits of damped Keplerian-like systems
The authors prove some stability results for planar systems of the type \[ \ddot x + h(t) \dot x + g(t) \frac{x}{|x|^{\alpha+1}}=0\,, \] where \(\alpha>0\), \(g,h:{\mathbb R}\to{\mathbb R}\) are continuous and \(T\)-periodic functions, with \[ \bar h:=\frac{1}{T}\int_0^T h(t)\,dt=0. \] Their aim is to establish some sufficient conditions for the existence of radially T-periodic collisionless solutions \(x:{\mathbb R}\to{\mathbb R}^2\setminus\{0\}\) which are Lyapunov stable in the radial direction. The results are new also for the Kepler problem, with \(h\equiv0\) and \(\bar g>0\).
scientific article; zbMATH DE number 7189397
scientific article