1,720,996 research outputs found
Integrable systems of quartic oscillators II
No full textSeveral completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion ("acceleration equal force"), with linear and cubic forces, in N-dimensional space (N being an arbitrary positive integer, with special attention to N = 2, namely, motions in a plane, and N = 3, namely, motions in ordinary three-dimensional space). All the equations of motion are written in covariant form ("N-vector equal N-vector"), entailing their rotational invariance. The corresponding Hamiltonians are of normal type, with the kinetic energy quadratic in the canonical momenta, and the potential energy quadratic and quartic in the canonical coordinates. (C) 2004 Elsevier B.V. All rights reserved
Integrability, analyticity, isochrony, equilibria, small oscillations, and Diophantine relations: results from the stationary Burgers hierarchy
No full textAn isochronous system is introduced by modifying the Nth ODE of the stationary Burgers hierarchy, and then, by investigating its behaviour near its equilibria, neat Diophantine relations are identified, involving (well-known) polynomials of arbitrary degree having integer zeros, or equivalently matrices the determinants of which yield such polynomials. The basic idea to arrive at such relations is not new, but the specific application reported in this paper is new, and it is likely to open the way to several analogous new findings
"On a method for computing eigenvalues and eigenfunctions of linear differential operators"
No full text- …
