A group theoretic approach to generalized harmonic vibrations in a one dimensional lattice.
Algebras of integrals
Generalized Whittaker's equations for holonomic mechanical systems.
Mouvements relatifs à la surface de la terre
Non-integrability of certain Hamiltonian systems. Applications of the Morales-Ramis differential Galois extension of Ziglin theory
The aim of this paper is to present two examples of non academic Hamiltonian systems for which the Morales-Ramis theory can be applied effectively. First, we investigate the Gross-Neveu system with n degrees of freedom. Till now it has been proved that this system is not integrable for n = 3. We give a simple proof that it is not completely integrable for an arbitrary n ≥ 3. Our second example is a natural generalisation of the Jacobi problem of a material point moving on an ellipsoid. We formulate...
On control problems of minimum time for Lagrangian systems similar to a swing. I. Convexity criteria for sets
One establishes some convexity criteria for sets in . They will be applied in a further Note to treat the existence of solutions to minimum time problems for certain Lagrangian systems referred to two coordinates, one of which is used as a control. These problems regard the swing or the ski.
On control problems of minimum time for Lagrangian systems similar to a swing. II Application of convexity criteria to certain minimum time problems
This Note is the Part II of a previous Note with the same title. One refers to holonomic systems with two degrees of freedom, where the part can schemetize a swing or a pair of skis and schemetizes whom uses . The behaviour of is characterized by a coordinate used as a control. Frictions and air resistance are neglected. One considers on minimum time problems and one is interested in the existence of solutions. To this aim one determines a certain structural condition which implies...
On the alpine ski with dry friction and air resistance. Some optimization problems for it
In the present work, divided in three parts, one considers a real skis-skier system, , descending along a straight-line with constant dry friction; and one schematizes it by a holonomic system , having any number of degrees of freedom and subjected to (non-ideal) constraints, partly one-sided. Thus, e.g., jumps and also «steps made with sliding skis» can be schematized by . Among the Lagrangian coordinates for two are the Cartesian coordinates and of its center of mass, , relative...
Periodic solutions to Lagrangian system
A classical mechanics Lagrangian system with even Lagrangian is considered. The configuration space is a cylinder . A large class of nonhomotopic periodic solutions has been found.
Some first integrals of differential equations of motion of a mechanical system.
Su di un sistema dissipativo soggetto a forze dipendenti dal tempo
Untersuchungen über die Bewegung eines Systemes starrer Körper