Multibump periodic motions of an infinite lattice of particles.
Se estudia la integrabilidad de campos multivectoriales en variedades diferenciables y la relación entre algunos tipos de campos multivectoriales en un fibrado de jets y conexiones en dicho fibrado. Como caso particular se relacionan los campos multivectoriales integrables y las conexiones cuyas secciones integrales son holonómicas. Como aplicación de todo ello, estos resultados permiten escribir las ecuaciones de campo de las teorías clásicas de campos de primer orden en varias formas equivalentes....
Let be the Lie group of all Euclidean motions in the Euclidean space , let be its Lie algebra and the space dual to . This paper deals with structures of the subspaces of which are formed by all the forces whose power exerted on the robot effector is zero.
We consider magnetic geodesic flows on the two-torus. We prove that the question of existence of polynomial in momenta first integrals on one energy level leads to a semi-Hamiltonian system of quasi-linear equations, i.e. in the hyperbolic regions the system has Riemann invariants and can be written in conservation laws form.
A new variational principle and duality for the problem Lu = ∇G(u) are provided, where L is a positive definite and selfadjoint operator and ∇G is a continuous gradient mapping such that G satisfies superquadratic growth conditions. The results obtained may be applied to Dirichlet problems for both ordinary and partial differential equations.
The dynamics of singular Lagrangean systems is described by a distribution the rank of which is greater than one and may be non-constant. Consequently, these systems possess two kinds of conserved functions, namely, functions which are constant along extremals (constants of the motion), and functions which are constant on integral manifolds of the corresponding distribution (first integrals). It is known that with the help of the (First) Noether theorem one gets constants of the motion. In this...