15,892 research outputs found
Quasivelocities and Optimal Control for Underactuated Mechanical Systems
This paper is concerned with the application of the theory of quasivelocities
for optimal control for underactuated mechanical systems. Using this theory, we
convert the original problem in a variational second-order lagrangian system
subjected to constraints. The equations of motion are geometrically derived
using an adaptation of the classical Skinner and Rusk formalism.Comment: 8 page
Towards a Hamilton-Jacobi Theory for Nonholonomic Mechanical Systems
In this paper we obtain a Hamilton-Jacobi theory for nonholonomic mechanical
systems. The results are applied to a large class of nonholonomic mechanical
systems, the so-called \v{C}aplygin systems.Comment: 13 pages, added references, fixed typos, comparison with previous
approaches and some explanations added. To appear in J. Phys.
Singular lagrangian systems and variational constrained mechanics on Lie algebroids
The purpose of this paper is describe Lagrangian Mechanics for constrained
systems on Lie algebroids, a natural framework which covers a wide range of
situations (systems on Lie groups, quotients by the action of a Lie group,
standard tangent bundles...). In particular, we are interested in two cases:
singular Lagrangian systems and vakonomic mechanics (variational constrained
mechanics). Several examples illustrate the interest of these developments.Comment: 42 pages, Section with examples improve
Quantum corrections to the geodesic equation
In this talk we will argue that, when gravitons are taken into account, the
solution to the semiclassical Einstein equations (SEE) is not physical. The
reason is simple: any classical device used to measure the spacetime geometry
will also feel the graviton fluctuations. As the coupling between the classical
device and the metric is non linear, the device will not measure the
`background geometry' (i.e. the geometry that solves the SEE). As a particular
example we will show that a classical particle does not follow a geodesic of
the background metric. Instead its motion is determined by a quantum corrected
geodesic equation that takes into account its coupling to the gravitons. This
analysis will also lead us to find a solution to the so-called gauge fixing
problem: the quantum corrected geodesic equation is explicitly independent of
any gauge fixing parameter.Comment: Revtex file, 6 pages, no figures. Talk presented at the meeting
"Trends in Theoretical Physics II", Buenos Aires, Argentina, December 199
Relevance of nonadiabatic effects in TiOCl
We analyze the effect of the phonon dynamics on a recently proposed model for
the uniform-incommensurate transition seen in TiOX compounds. The study is
based on a recently developed formalism for nonadiabatic spin-Peierls systems
based on bosonization and a mean field RPA approximation for the interchain
coupling. To reproduce the measured low temperature spin gap, a spin-phonon
coupling quite bigger than the one predicted from an adiabatic approach is
required. This high value is compatible with the renormalization of the phonons
in the high temperature phase seen in inelastic x-ray experiments. Our theory
accounts for the temperature of the incommensurate transition and the value of
the incommensurate wave vector at the transition point.Comment: 4 pages, 2 figure
Variational integrators and time-dependent lagrangian systems
This paper presents a method to construct variational integrators for
time-dependent lagrangian systems. The resulting algorithms are symplectic,
preserve the momentum map associated with a Lie group of symmetries and also
describe the energy variation.Comment: 8 page
Reduced classical field theories. k-cosymplectic formalism on Lie algebroids
In this paper we introduce a geometric description of Lagrangian and
Hamiltonian classical field theories on Lie algebroids in the framework of
-cosymplectic geometry. We discuss the relation between Lagrangian and
Hamiltonian descriptions through a convenient notion of Legendre
transformation. The theory is a natural generalization of the standard one; in
addition, other interesting examples are studied, mainly on reduction of
classical field theories.Comment: 26 page
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