4 citations · 9 across the 12 of their papers we have counts for
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A new class of separable Lagrangian systems generalizing Sawada-Kotera
Gianluca Gorni, Mattia Scomparin, Gaetano Zampieri
Some characteristics of the Sawada-Kotera Lagrangian system lend themselves to generalization, producing a large class of separable Lagrangian systems with two degrees of freedom.
The geodesics for Poincaré's half-plane: a nonstandard derivation
Gianluca Gorni, Gaetano Zampieri
Constants of motion are usually derived from groups of symmetry transformation of the system. Here we show that useful properties of the system can be deduced from a family of Noet…
Nonlocal constants of motion in Lagrangian Dynamics of any order
Gianluca Gorni, Mattia Scomparin, Gaetano Zampieri
We describe a recipe to generate "nonlocal" constants of motion for ODE Lagrangian systems. As a sample application, we recall a nonlocal constant of motion for dissipative mechani…
Lagrangian dynamics by nonlocal constants of motion
Gianluca Gorni, Gaetano Zampieri
A simple general theorem is used as a tool that generates nonlocal constants of motion for Lagrangian systems. We review some cases where the constants that we find are useful in t…
On-flow and strong solutions to Killing-type equations
Gianluca Gorni, Gaetano Zampieri
If we impose infinitesimal invariance up to a boundary term of the action functional for Lagrangian ordinary differential equations, we are led to Killing-type equations, which are…
Weak instability of Hamiltonian equilibria
Gaetano Zampieri
This is an expository paper on Lyapunov stability of equilibria of autonomous Hamiltonian systems. Our aim is to clarify the concept of weak instability, namely instability without…
Global isochronous potentials
Gianluca Gorni, Gaetano Zampieri
We present a geometric characterization of the nonlinear smooth functions for which the origin is a global isochronous center for the scalar equation .…
Nonholonomic versus vakonomic dynamics
Gaetano Zampieri
The main aim of the present paper is to raise the doubt that vakonomic dynamics may not be satisfactory as a model for velocity dependent constraints.
Completely integrable Hamiltonian systems with weak Lyapunov instability or isochrony
Gaetano Zampieri
The aim of this paper is to introduce a class of Hamiltonian autonomous systems in dimension 4 which are completely integrable and their dynamics is described in all details. They…