<i>Classical Mechanics</i>

Corben, H. C.; Stehle, P.; Beiser, Arthur

doi:10.1063/1.3061288

Cited by 41 publications

(65 citation statements)

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“…͑1.1͒ for a variety of interaction potentials. We use classical dynamics [24][25][26] ͓͗p ͘ , H͔͒ is equal to zero. It is of interest to determine the locus in phase space where the latter quantity vanishes, i.e., where the adiabatic approximation applies.…”

Section: ͑Ii͒mentioning

confidence: 99%

Adiabatic invariance along the reaction coordinate

Lorquet

2009

The Journal of Chemical Physics

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Classical trajectory and statistical adiabatic channel study of the dynamics of capture and unimolecular bond fission. IV. Valence interactions between atoms and linear rotors J. Chem. Phys. 108, 5265 (1998) In a two-dimensional space where a point particle interacts with a diatomic fragment, the action integral ͛p d ͑where is the angle between the fragment and the line of centers and p its conjugate momentum͒ is an adiabatic invariant. This invariance is thought to be a persistent dynamical constraint. Indeed, its classical Poisson bracket with the Hamiltonian is found to vanish in particular regions of the potential energy surface: asymptotically, at equilibrium geometries, saddle points, and inner turning points, i.e., at remarkable situations where the topography of the potential energy surface is locally simple. Studied in this way, the adiabatic decoupling of the reaction coordinate is limited to disjoint regions. However, an alternative view is possible. The invariance properties of entropy ͑as defined in information theory͒ can be invoked to infer that dynamical constraints that are found to operate locally subsist everywhere, throughout the entire reactive process, although with a modified expression.

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Section: ͑Ii͒mentioning

confidence: 99%

Adiabatic invariance along the reaction coordinate

Lorquet

2009

The Journal of Chemical Physics

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“…The analysis of the dynamical behavior of a simple inverted pendulum has been studied in connection with stability problems, both from a theoretical and experimental viewpoint and with delay [1][2][3][4][5][6]. However, analytical solutions of the problem assuming oscillations in the suspension point are only considered under certain simplifications in the problem, as it appears in Ref [2].…”

Section: Introductionmentioning

confidence: 99%

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

Pérez-Polo

Molina

Chica

et al. 2014

Applied Mathematics and Computation

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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.

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“…It can be make with a rigid rod which rotates in a vertical plane: Stephenson (1908), Phelps & Hunter (1965), Blitzer (1965), Friedman (1982) and Douvropoulos (2012). The inverted pendulum has the remarkable property to be stable in a vertical position when the supporting point oscillates vertically above a certain frequency: Corben & Stehle (1994) and Semenov el al. (2013).…”

Section: Introductionmentioning

confidence: 99%

HEAd'15 - International Conference on Higher Education Advances - Proceedings

Poza

Domènech

Lloret

et al. 2015

HEAd'15. Conference on Higher Education Advances

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PrefaceThis volume contains the proceedings of the First International Conference on Higher Education Advances (HEAd'15), which was held in Valencia, Spain during 24-26 June 2015. HEAd aims to become a forum for researchers and practitioners to exchange ideas, experiences, opinions and research results relating to the preparation of students and the organization of educational systems. The conference was hosted by the Faculty of Business Administration and Management of the Universitat Politècncia de València.The conference featured three invited speakers who overviewed important and actual topics: John Kalu Osiri (Washington State University) delivered the presentation on the indispensable role of educators in shaping a nation, Ana Muñoz-Miquel (Universitat Jaume I) on how to bridge the gap between professional practice and university education, and José V. Benlloch-Dualde (Universitat Politècnica de València) on effective ways to enhance collaboration in the classroom.Following the call for papers, HEAd'15 received 165 submissions with authors representing 41 different countries. Papers went through a rigorous review process. Each paper was reviewed by at least two program committee members. Finally, 50 submissions were selected as full papers (representing an acceptance rate of 30%) and 22 submissions were selected as short papers. Additionally, 20 papers were selected to be presented as posters.I would like to thank all the people and institutions who contributed to the success of the HEAd'15 conference: the authors, the members of the program committee as well as the additional reviewers, the invited speakers, the members of the organizing committee, and the sponsors. I am also grateful to Abstract: The international accreditation for the Master and Bachelor degrees offered at our university, together with the demands of the employers, have made it clear that the students' curricula should specify not only what they have studied, but also what they are actually able to do. Although the competence based curricula approach has been used in the development of the new programmes for the Master and Bachelor degrees within the European Higher Education Area in recent years, the assessment of these competences is still a pending task. This work presents an 'outcomes' approach for the assessment of the oral and written communication skills within subjects related to mechanical and materials engineering. In particular, this paper proposes some rubrics developed in order to quantify the level of achievement. These rubrics are based on the evaluation of some learning outcomes that can be observed by using different strategies during the course. Conclusions about preliminary results and the difficulties found in order to create these tools are also described here.

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Classical Mechanics

Cited by 41 publications

References 0 publications

Adiabatic invariance along the reaction coordinate

Adiabatic invariance along the reaction coordinate

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

HEAd'15 - International Conference on Higher Education Advances - Proceedings

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