The Kowalevski's top and the method of Syzygies
A new algorithm for finding separation coordinates is tested on the example of Kowalev ski’s top.
The Lagrangian and Hamiltonian formulations for the waves in a compressible fluid with the Hall current.
In questo lavoro si ricavano: 1) l'equazione d'onda linearizzata, 2) la formulazione Lagrangiana, 3) la formulazione Hamiltoniana, nella teoria della propagazione ondosa in un fluido comprimibile descritto dalle equazioni della magnetofluidodinamica ideale in presenza di corrente Hall.
The Legendre transformation
The magnetic geodesic flow in a homogeneous field on the complex projective space.
The -centre problem of celestial mechanics for large energies
We consider the classical three-dimensional motion in a potential which is the sum of attracting or repelling Coulombic potentials. Assuming a non-collinear configuration of the centres, we find a universal behaviour for all energies above a positive threshold. Whereas for there are no bounded orbits, and for there is just one closed orbit, for the bounded orbits form a Cantor set. We analyze the symbolic dynamics and estimate Hausdorff dimension and topological entropy of this hyperbolic set....
The obstacle problem and direct products of unfurled swallowtails
The quantum stability problem for time-periodic perturbations of the harmonic oscillator
The reduction of symplectic structure and Sternberg construction
The shadowing chain lemma for singular Hamiltonian systems involving strong forces
We consider a planar autonomous Hamiltonian system :q+∇V(q) = 0, where the potential V: ℝ2 {ζ→ ℝ has a single well of infinite depth at some point ζ and a strict global maximum 0at two distinct points a and b. Under a strong force condition around the singularity ζ we will prove a lemma on the existence and multiplicity of heteroclinic and homoclinic orbits - the shadowing chain lemma - via minimization of action integrals and using simple geometrical arguments.
The symmetric tensor Lichnerowicz algebra and a novel associative Fourier-Jacobi algebra.
The symmetry reduction of variational integrals
The Routh reduction of cyclic variables in the Lagrange function and the Jacobi-Maupertuis principle of constant energy systems are generalized. The article deals with one-dimensional variational integral subject to differential constraints, the Lagrange variational problem, that admits the Lie group of symmetries. Reduction to the orbit space is investigated in the absolute sense relieved of all accidental structures. In particular, the widest possible coordinate-free approach to the underdetermined...
The symmetry reduction of variational integrals, complement
Some open problems appearing in the primary article on the symmetry reduction are solved. A new and quite simple coordinate-free definition of Poincaré-Cartan forms and the substance of divergence symmetries (quasisymmetries) are clarified. The unbeliavable uniqueness and therefore the global existence of Poincaré-Cartan forms without any uncertain multipliers for the Lagrange variational problems are worth extra mentioning.
The symplectic structure of curves in three dimensional spaces of constant curvature and the equations of mathematical physics
The variational principle for the uniform acceleration and quasi-spin in two dimensional space-time.
Topology and Mechanics. II. The Planar n-Body Problem.
Totally singular Lagrangians and affine Hamiltonians.
Trajectoires bornées d'une particule soumise à un champ magnétique symétrique linéaire
Trajectoires bornées d'une particule soumise à un champ magnétique symétrique linéaire
Transformations canoniques des systèmes dégénérés.
Transformations canoniques linéaires dans les espaces de Hilbert