759 research outputs found
Controlling Multiparticle System on the Line, II - Periodic case
As in arXiv: math. 0809.2365 we consider classical system of interacting
particles on the line with only neighboring
particles involved in interaction. On the contrast to arXiv: math. 0809.2365
now {\it periodic boundary conditions} are imposed onto the system, i.e.
and are considered neighboring. Periodic Toda
lattice would be a typical example. We study possibility to control periodic
multiparticle systems by means of forces applied to just few of its particles;
mainly we study system controlled by single force. The free dynamics of
multiparticle systems in periodic and nonperiodic case differ substantially. We
see that also the controlled periodic multiparticle system does not mimic its
non-periodic counterpart.
Main result established is global controllability by means of single
controlling force of the multiparticle system with ageneric potential of
interaction. We study the nongeneric potentials for which controllability and
accessibility properties may lack. Results are formulated and proven in
Sections~2,3.Comment: 15 page
- β¦