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math.DS2026
Relative equilibria, linear stability and electromagnetic curvature
Luca Asselle, Giorgia Testolina
In this paper we study the linear stability of relative equilibria in the Newtonian -body problem from the viewpoint of electromagnetic systems. We first examine the effect of t…
math.DS2026
Non-minimality and instability of brake orbits for natural Lagrangians on Riemannian manifolds
Luca Asselle, Xijun Hu, Alessandro Portaluri +1
We investigate minimality and stability of periodic brake orbits in natural Lagrangian systems on smooth Riemannian manifolds. We prove that every non-constant periodic brake orbit…
math.DS2024
On the Zoll deformations of the Kepler problem
Asselle Luca, Baranzini Stefano
A celebrated result of Bertrand states that the only central force potentials on the plane with the property that all bounded orbits are periodic are the Kepler potential and the p…