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Synchronization of two coupled pendula in absence of escapement

Applied Mathematics and Mechanics(English Edition) 2016年第12期37卷 1721-1738页

作者： f.talamucci DIMAI Dipartimento di Matematica e Informatica "Ulisse Dini"Università degli Studi di Firenze

A model of two oscillating pendula placed on a mobile support is studied. Once an overall scheme of equations, under general assumptions, is formulated via the Lagrangian equations of motion, the specific case of absence of escapement is examined. The mechanical model consists of two coupled pendula both oscillating on a moving board attached to a spring. The final result performs selection among the peculiar parameters of the physical process （the length, the ratio of masses, the friction and damping coefficients, and the stiffness of the spring）, providing a tendency to synchronization.

关键词： synchronization coupled pendula characteristic equation eigenvalue lo-calization

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Motion of Nonholonomous Rheonomous Systems in the Lagrangian formalism

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Journal of Applied Mathematics and Physics 2015年第3期3卷 295-309页

作者： f. talamucci DIMAI Dipartimento di Matematica e Informatica “Ulisse Dini” Università Degli Studi di Firenze Florence Italy

The main purpose of the paper consists in illustrating a procedure for expressing the equations of motion for a general time-dependent constrained system. Constraints are both of geometrical and differential type. The use of quasi-velocities as variables of the mathematical problem opens the possibility of incorporating some remarkable and classic cases of equations of motion. Afterwards, the scheme of equations is implemented for a pair of substantial examples, which are presented in a double version, acting either as a scleronomic system and as a rheonomic system.

关键词： Nonholonomous Systems Rheonomic Constraints Quasi-Velocites Appell and Boltzmann-Hamel Equations

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The Lagrangian Method for a Basic Bicycle

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Journal of Applied Mathematics and Physics 2014年第4期2卷 46-60页

作者： f. talamucci DIMAI Dipartimento di Matematica e Informatica “Ulisse Dini” Università degli Studi di Firenze Firenze Italy

The ground plan in order to disentangle the hard problem of modelling the motion of a bicycle is to start from a very simple model and to outline the proper mathematical scheme: for this reason the first step we perform lies in a planar rigid body (simulating the bicylcle frame) pivoting on a horizontal segment whose extremities, subjected to nonslip conditions, oversimplify the wheels. Even in this former case, which is the topic of lots of papers in literature, we find it worthwhile to pay close attention to the formulation of the mathematical model and to focus on writing the proper equations of motion and on the possible existence of conserved quantities. In addition to the first case, being essentially an inverted pendulum on a skate, we discuss a second model, where rude handlebars are added and two rigid bodies are joined. The geometrical method of Appell is used to formulate the dynamics and to deal with the nonholonomic constraints in a correct way. At the same time the equations are explained in the context of the cardinal equations, whose use is habitual for this kind of problems. The paper aims to a threefold purpose: to formulate the mathematical scheme in the most suitable way (by means of the pseudovelocities), to achieve results about stability, to examine the legitimacy of certain assumptions and the compatibility of some conserved quantities claimed in part of the literature.

关键词： Nonholomic Constraints Lagrangian Equations Pseudovelocities Nonlinear Order Differential Equations Stability

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Consonance of Complex Tones with Harmonics of Different Intensity

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Open Journal of Acoustics 2014年第2期4卷 78-89页

作者： Antonio Bernini federico talamucci Dipartimento di Matematica e Informatica “U. Dini” (DIMAI) Universita di Firezne Firenze Italy

The starting point of this study is the theory of tonal consonance by Plomp and Levelt. The major reference point is the theory of Critical Band and its use for evaluating consonance of simple tones. On the basis of such empirical criterion, our aim consists in providing a method of estimating the value of consonance of complex tones, by taking account not only of the number of harmonics, but also of the intensity of the partials which contribute to forming the tone. By introducing a specific algorithm, the level of consonance of a chord of complex tones is expressed in terms both of frequency differences and sound intensity of the partials. The results give rise to a series of considerations and applications, ranging from displaying the order of consonance of all intervals within the octave up to evaluating the hierarchy of chords in the frame of a musical scale.

关键词： Consonance Complex Tones Scale Critical Bandwidth Intensity of Harmonics Loudness

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