3,838 research outputs found
Nonholonomic constraints in -symplectic Classical Field Theories
A -symplectic framework for classical field theories subject to
nonholonomic constraints is presented. If the constrained problem is regular
one can construct a projection operator such that the solutions of the
constrained problem are obtained by projecting the solutions of the free
problem. Symmetries for the nonholonomic system are introduced and we show that
for every such symmetry, there exist a nonholonomic momentum equation. The
proposed formalism permits to introduce in a simple way many tools of
nonholonomic mechanics to nonholonomic field theories.Comment: 27 page
Coherent delocalization: Views of entanglement in different scenarios
The concept of entanglement was originally introduced to explain correlations
existing between two spatially separated systems, that cannot be described
using classical ideas. Interestingly, in recent years, it has been shown that
similar correlations can be observed when considering different degrees of
freedom of a single system, even a classical one. Surprisingly, it has also
been suggested that entanglement might be playing a relevant role in certain
biological processes, such as the functioning of pigment-proteins that
constitute light-harvesting complexes of photosynthetic bacteria. The aim of
this work is to show that the presence of entanglement in all of these
different scenarios should not be unexpected, once it is realized that the very
same mathematical structure can describe all of them. We show this by
considering three different, realistic cases in which the only condition for
entanglement to exist is that a single excitation is coherently delocalized
between the different subsystems that compose the system of interest
Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries
We state the intrinsic form of the Hamiltonian equations of first-order
Classical Field theories in three equivalent geometrical ways: using
multivector fields, jet fields and connections. Thus, these equations are given
in a form similar to that in which the Hamiltonian equations of mechanics are
usually given. Then, using multivector fields, we study several aspects of
these equations, such as the existence and non-uniqueness of solutions, and the
integrability problem. In particular, these problems are analyzed for the case
of Hamiltonian systems defined in a submanifold of the multimomentum bundle.
Furthermore, the existence of first integrals of these Hamiltonian equations is
considered, and the relation between {\sl Cartan-Noether symmetries} and {\sl
general symmetries} of the system is discussed. Noether's theorem is also
stated in this context, both the ``classical'' version and its generalization
to include higher-order Cartan-Noether symmetries. Finally, the equivalence
between the Lagrangian and Hamiltonian formalisms is also discussed.Comment: Some minor mistakes are corrected. Bibliography is updated. To be
published in J. Phys. A: Mathematical and Genera
A Generalization of Chetaev's Principle for a Class of Higher Order Non-holonomic Constraints
The constraint distribution in non-holonomic mechanics has a double role. On
one hand, it is a kinematic constraint, that is, it is a restriction on the
motion itself. On the other hand, it is also a restriction on the allowed
variations when using D'Alembert's Principle to derive the equations of motion.
We will show that many systems of physical interest where D'Alembert's
Principle does not apply can be conveniently modeled within the general idea of
the Principle of Virtual Work by the introduction of both kinematic constraints
and variational constraints as being independent entities. This includes, for
example, elastic rolling bodies and pneumatic tires. Also, D'Alembert's
Principle and Chetaev's Principle fall into this scheme. We emphasize the
geometric point of view, avoiding the use of local coordinates, which is the
appropriate setting for dealing with questions of global nature, like
reduction.Comment: 27 pages. Journal of Mathematical Physics (to zappear
Higher-order Mechanics: Variational Principles and other topics
After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the
Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we
state a unified geometrical version of the Variational Principles which allows
us to derive the Lagrangian and Hamiltonian equations for these kinds of
systems. Then, the standard Lagrangian and Hamiltonian formulations of these
principles and the corresponding dynamical equations are recovered from this
unified framework.Comment: New version of the paper "Variational principles for higher-order
dynamical systems", which was presented in the "III Iberoamerican Meeting on
Geometry, Mechanics and Control" (Salamanca, 2012). The title is changed. A
detailed review is added. Sections containing results about variational
principles are enlarged with additional comments, diagrams and summarizing
results. Bibliography is update
On the Hamilton-Jacobi Theory for Singular Lagrangian Systems
We develop a Hamilton-Jacobi theory for singular lagrangian systems using the
Gotay-Nester-Hinds constraint algorithm. The procedure works even if the system
has secondary constraints.Comment: 36 page
El rechazo del desarrollo sostenible : ¿una crítica justificada?
El concepto de desarrollo sostenible surge por vía negativa, como resultado de los análisis de la actual situación de emergencia planetaria, que amenaza gravemente el futuro de la humanidad, y se contrapone explícitamente al de crecimiento sostenido, radicalmente insostenible en un mundo finito. Pero este concepto ha sufrido graves desvirtuaciones en su manejo, dando lugar a críticas procedentes incluso de la educación ambiental. En la comunicación se describe la estrategia diseñada para hacer frente a los malentendidos en torno al desarrollo sostenible y se presentan los resultados obtenidos, que muestran la posibilidad de salir al paso de las interpretaciones distorsionadas, poniendo de manifiesto que entre Educación ambiental y Educación para la sostenibilidad no existe oposición, sino, muy al contrario, el mismo objetivo de hacer posible un futuro sostenible
Design of a Software System to Support Value Education in Sports Through Gamification Techniques
Nowadays, it is quite common to find violent acts in grassroot sports, such as football. Almost every week, it is possible to find news about team supporters fighting against each other, or football players arguing aggressively to the referee. And the worst part in this story is that most of these acts are watched by children. In order to alleviate this situation and create awareness of the necessity to create educational programs to prevent violence in sports, the European Union has funded several projects focused on this area. One of this project is called SAVEit project, and its goal is to create and develop innovative educational tools to promote values in grassroot sports. This paper presents the software architecture designed in SAVEit project to achieve this goal. This architecture is mainly composed of a
Learning Management System, where coaches will learn about the values; a Team Management Site, where coaches can evaluate the values acquired by the children of the teams; and finally, a Video Game that using gamification techniques will keep the motivation of children during the learning process
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