scholarly journals VIRTUAL LABORATORIES AS STRATEGY FOR TEACHING IMPROVEMENT IN MATH SCIENCES AND ENGINEERING IN BOLIVIA

2020 ◽  
Vol 2 (1) ◽  
pp. 52-62
Author(s):  
Francisco Vargas
Keyword(s):  
Differential Equations ◽  
Matrix Algebra ◽  
Degrees Of Freedom ◽  
Inverted Pendulum ◽  
Numerical Algorithms ◽  
Three Dimensions ◽  
Technological Advancement ◽  
Teaching Improvement ◽  
Two Degrees Of Freedom ◽  
Virtual Laboratories

The vertiginous technological advancement has made necessary the use of computersoftware that contributes to the improvement of teaching in math sciences and engineering.It is in this context that the last five years the strategy presented in this article has been disseminatedin the main universities of Bolivia, a country where the schools have not yet been ableto offer basic disciplines such as calculus, matrix algebra, physics and/or differential equationsto solve problems considering applicative aspects. To establish this connection, it is necessaryto deduce differential equations associated with practical problems, solve these equationswith different numerical algorithms, and establish the concept of simulation to later introducelanguages like Python/VPython free of license to elaborate Virtual Laboratories that allow obtainingthe solutions in two and three dimensions. The classical problems addressed for thispurpose are the satellite of two degrees of freedom and the inverted pendulum.

scholarly journals Virtual laboratories as strategy for teaching improvement in Math Sciences and Engineering in Bolivia

2021 ◽  
Vol 14 (2) ◽  
pp. 187-196
Author(s):  
Francisco Javier Triveno Vargas ◽  
Hugo Siles Alvarado
Keyword(s):  
Differential Equations ◽  
Programming Languages ◽  
Stem Education ◽  
Degrees Of Freedom ◽  
Classical Problem ◽  
Interdisciplinary Approach ◽  
Theory And Practice ◽  
Relevant Today ◽  
Virtual Laboratories ◽  
And Mathematics

STEM education is a strategy based on four disciplines (science, technology, engineering and mathematics), integrated in an innovative interdisciplinary approach. Although, the concept of STEM education is more relevant today, the discussion of a teaching model with special attention in the four subjects aforementioned began in the early 2000s. Taking into account this context, the strategy presented in this paper has been disseminated in Bolivia’s main universities for the last five years. A country that has not yet managed to associate basic disciplines such as calculus, matrix algebra, and/or differential equations to solve problems of an applicative nature, that is, to establish the link between theory and practice. To establish the connection, it is necessary to deduce differential equations associated with practical problems; solve these equations with numerical methods, appeal to the simulation concept to later introduce programming languages like Python/VPython to build virtual laboratories. The classical problem addressed for this purpose is the satellite of two degrees of freedom.

Optimal parameters of tuned mass dampers for an inverted pendulum with two degrees of freedom

2020 ◽  
pp. 146441932097108
Author(s):  
Duy-Chinh Nguyen
Keyword(s):  
Degrees Of Freedom ◽  
Inverted Pendulum ◽  
Tall Buildings ◽  
Viscous Resistance ◽  
Optimal Parameters ◽  
Tuned Mass Dampers ◽  
Two Degrees Of Freedom ◽  
Resistance Method ◽  
Parametric Studies ◽  
Frequency Ratios

In reality, an inverted pendulum can be used to model many real structures as the fluid tower, super-tall buildings, or articulated tower in the ocean, etc. However, for the inverted pendulum with two degrees of freedom, to the best knowledge of the author, there is no study to determine optimal parameters of two tuned mass dampers (TMD) by using the maximization of equivalent viscous resistance method. Therefore, the current study presents the analytical solutions to the optimization of two orthogonal TMDs, which is used to eliminate vibration of the inverted pendulum with two degrees of freedom. The parameters considered in optimizing are the natural frequency ratios and damping ratios of the two TMDs. The new results of this paper can be summarized as follows: Firstly, the equivalent resistance forces of the two TMDs acting on the inverted pendulum with two degrees of freedom are established. Secondly, the quadratic torque matrices of the vibration response of the inverted pendulum attached with two TMDs is revealed. Thirdly, the optimal expressions are derived using the maximization of equivalent viscous resistance method. The obtained formulae provide exact solutions for the proposed problem. Finally, to confirm the effectiveness of the obtained formulae, parametric studies on vibration are performed for sample articulated tower in the ocean with and without optimal TMDs. Numerical results show that vibrations of the articulated tower attached with optimal TMDs are effectively eliminated. This confirms that the optimal parameters of the two TMDs are determined in this paper are reliable and accurate.

scholarly journals The Vibrations of a Particle about a Position of Equilibrium—Part 2 :The Relation between the Elliptic Function and Series Solutions

1921 ◽  
Vol 40 ◽  
pp. 34-49 ◽  
Author(s):  
Bevan B. Baker
Keyword(s):  
Dynamical System ◽  
Differential Equations ◽  
Elliptic Function ◽  
Degrees Of Freedom ◽  
Elliptic Functions ◽  
Series Solutions ◽  
Two Degrees Of Freedom ◽  
Function Solution

In a previous paper, entitled the “Vibrations of a Particle about a Position of Equilibrium,” by the author in collaboration with Professor E. B. Ross (Proc. Edin. Math. Soc., XXXIX, 1921, pp. 34–57), a particular dynamical system having two degrees of freedom was chosen and solutions of the corresponding differential equations were obtained in terms of periodic series and also in terms of elliptic functions. It was shown that for certain values of the frequencies of the principal vibrations, the periodic series become divergent, whereas the elliptic function solution continues to give finite results.

Lyapunov Functions and Sliding Mode Control for Two Degrees-of-Freedom and Multidegrees-of-Freedom Fractional Oscillators

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Youan Zhang ◽  
Jian Yuan ◽  
Jingmao Liu ◽  
Bao Shi
Keyword(s):  
Differential Equations ◽  
Sliding Mode Control ◽  
Lyapunov Functions ◽  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Equations Of Motion ◽  
Control Design ◽  
State Equations ◽  
Two Degrees Of Freedom ◽  
Mode Control

This paper addresses the Lyapunov functions and sliding mode control design for two degrees-of-freedom (2DOF) and multidegrees-of-freedom (MDOF) fractional oscillators. First, differential equations of motion for 2DOF fractional oscillators are established by adopting the fractional Kelvin–Voigt constitute relation for viscoelastic materials. Second, a Lyapunov function candidate for 2DOF fractional oscillators is suggested, which includes the potential energy stored in fractional derivatives. Third, the differential equations of motion for 2DOF fractional oscillators are transformed into noncommensurate fractional state equations with six dimensions by introducing state variables with physical significance. Sliding mode control design and adaptive sliding mode control design are proposed based on the noncommensurate fractional state equations. Furthermore, the above results are generalized to MDOF fractional oscillators. Finally, numerical simulations are carried out to validate the above control designs.

scholarly journals VII.—On the Adelphic Integral of the Differential Equations of Dynamics

1918 ◽  
Vol 37 ◽  
pp. 95-116 ◽  
Author(s):  
E. T. Whittaker
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Two Degrees Of Freedom ◽  
Image Position ◽  
Kinetic And Potential Energies

§ 1. Ordinary and singular periodic solutions of a dynamical system. — The present paper is concerned with the motion of dynamical systems which possess an integral of energy. To fix ideas, we shall suppose that the system has two degrees of freedom, so that the equations of motion in generalised co-ordinates may be written in Hamilton's formwhere (q1q2) are the generalised co-ordinates, (p1, p2) are the generalised momenta, and where H is a function of (q1, q2, p1, p2) which represents the sum of the kinetic and potential energies.

scholarly journals The interference galloping of two circular cylinders with equal diameters.

2007 ◽  
Vol 1 (1) ◽  
pp. 087-102
Author(s):  
Ewa Błazik-Borowa
Keyword(s):  
Differential Equations ◽  
Turbulence Intensity ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Numerical Analyses ◽  
Circular Cylinders ◽  
Two Degrees Of Freedom

The paper deals with numerical analyses of interference galloping of two elasticcaly supported circular cylinders of equal diameters. The basis of the analyses is a quasi-steady model of this phenomenon. The model assumes that both cylinders participate in the process of interference galloping and they have two degrees of freedom. The movement of the cylinders is described as a set of four nonlinear differential equations. On the basis of numerical solutions of these equations the author evaluate the correctness of this quasi-steady model. Then they estimate the dependence of a critical reduced velocity on the Scruton number, turbulence intensity and arrangements of the cylinders.

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