Note on an apparently forgotten theorem about solid rigid dynamics

We re-derive a general procedure to substitute any rigid body by an equivalent system of exactly four masses, located at the vertices of an irregular tetrahedron

Path tracking and stability of a rolling controlled wheel on a horizontal plane by using the nonholonomic constraints

This paper studies the stabilization, tracking of a predefined trajectory and how to reach a desired set point for a wheel which is rolling on a horizontal plane without slipping. For this purpose, the wheel is controlled by small torque generated by internal servomechanisms whose dynamics can be neglected. An efficient procedure to determine the kinetic energy of the wheel is developed by introducing a set of reference systems, which in combination with the Lagrange equations with multipliers allow deriving the mathematical model of the rolling wheel. In this model, the Euler angles, the coordinates of the plane–wheel contact point and a control law of proportional+integral+derivative (PID) type provide an efficient computational procedure to track arbitrary trajectories. It is shown that the nonholonomic constraints are fulfilled with admissible reaction forces, even when the desired trajectory has cusp points. A circumference and a family of astroids are used as trajectories to verify the motion conditions derived from the energy conservation and dynamical equilibrium of the wheel along such trajectories. The results of the analytical calculations are corroborated through numerical simulations

Estimation of the virial coefficients by means of chaotic oscillations of pressure and density: Application to quantum gases with cubic equations of state

This paper analyzes how to determine the virial coefficients B and C of real gases by using a theoretical device whose pressures and densities oscillate in chaotic regime. The device is formed by a valve, a pressure controller, a pressure probe and a gas accumulator, for which the thermodynamic model has been derived from the force-mass-energy balances. This model allows keeping the gas temperature almost constant with chaotic oscillations in the inlet to the accumulator. The chaotic data are used to obtain variability in the pressures and densities, so that they can be used as experimental values from which the virial coefficients are estimated. For this purpose, several cubic and high precision equations of state for polar and non-polar gases and mixtures are used. In particular, the virial coefficient B for dry air is estimated by using high precision state equations, whereas, the virial coefficients B and C are also estimated for quantum gases (He4, He3 H2, D2, Ne) by using several modified cubic equations of state at moderate and high pressures. Furthermore, the values for the virial coefficient B obtained from numerical simulations are used to estimate the intermolecular potential and the radial distribution function. The results are in good agreement with the currently known experimental data for virial coefficients published in the literature

Stability and chaotic behavior of a PID controlled inverted pendulum subjected to harmonic base excitations by using the normal form theory

In this paper we investigate the stability and the onset of chaotic oscillations around the pointing-up position for a simple inverted pendulum that is driven by a control torque and is harmonically excited in the vertical and horizontal directions. The driven control torque is defined as a proportional plus integral plus derivative (PID) control of the deviation angle with respect to the pointing-down equilibrium position. The parameters of the PID controller are tuned by using the Routh criterion to obtain a stable weak focus around the pointing-up position, whose stability is investigated by using the normal form theory. The normal form theory is also used to deduce a simplified mathematical model that can be resolved analytically and compared with the numerical simulation of the complete mathematical model. From the harmonic prescribed motions for the pendulum base, necessary conditions for chaotic motion are deduced by means of the Melnikov function. When the pendulum is close to the unstable pointing-up position, the PID parameters are changed and the chaotic motion is destroyed, which is achieved by employing very small control signals even in the presence of random noise. The results of the analytical calculations are verified by full numerical simulations

Los números naturales en el Aula de Primaria

Departament d'Educació. Codi d’assignatura: MP100

La geometría y la estadística en el aula de primaria

Departament d'Educació. Codi d’assignatura: MP102

La hegemonía cultural del glolugar: entre la relegación y la reivindicación local. El caso de Valencia

El artículo tiene por objeto abordar cómo la hegemonía del glolugar, en tanto que figura paradigmática de los procesos urbanos neoliberales, ha implicado un determinado modelo de política cultural y de desarrollo urbano que hemos podido singularizar en el caso de la ciudad de Valencia y la Ciudad de las Artes y de las Ciencias. La hegemonía cultural del glolugar no se puede entender sin enmarcarla en una tendencia global como es la extensión del urbanismo neoliberal, la ciudad es concebida como una entidad competitiva inmersa en un espacio global que promueve el mercado y la mentalidad emprendedora a través de nuevas prácticas de la gestión pública. En el caso de Valencia, el proyecto de ciudad neoliberal ha pivotado sobre los grandes proyectos y eventos, con la espectacular Ciudad de las Artes y de las Ciencias como mascarón de proa. Nuestra reflexión pretende vincular urbanismo neoliberal, política cultural y modelo de ciudad, utilizando como clave de bóveda el rol que el glolugar en nuestro caso la Ciudad de las Artes y de las Ciencias, tiene en el proceso. Sin embargo, frente a las políticas neoliberales del glolugar se ha ido conformando desde los barrios populares una serie de acciones socio-culturales desarrolladas por una red de asociaciones, grupos, colectivos e iniciativas culturales. Estas respuestas, unas más profesionales y otras más críticas con dicho modelo, ahora en crisis, proponen iniciativas culturales resistentes y alternativas

Els nombres naturals a l'aula de Primària

Departament d'Educació. Codi d’assignatura: MP100

La construcció del pensament matemàtic en l’educació infantil

Departament d' Educació. Codi d’assignatura: MI101

Los números enteros y racionales, las magnitudes y la medida en el aula de primaria

Departament d'Educació. Codi d’assignatura: MP101