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Did you mean equation AND differential?

Duggen, L.; Willatzen, M.; Voon, L. C. Lew Yan – European Journal of Physics, 2012

This paper illustrates both a problem in mathematical physics, whereby the method of separation of variables, while applicable, leads to three ordinary differential equations that remain fully coupled via two separation constants and a five-term recurrence relation for series solutions, and an exactly solvable problem in electrostatics, as a…

Descriptors: Mathematics, Physics, Calculus, Equations (Mathematics)

Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada – European Journal of Physics, 2009

A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…

Descriptors: Calculus, Equations (Mathematics), Computation, Equipment

Provost, J.-P.; Bracco, C. – European Journal of Physics, 2009

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non-trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple…

Descriptors: Motion, Secondary School Teachers, Equations (Mathematics), Mathematics Instruction

Ochs, Karlheinz – European Journal of Physics, 2011

In this paper, an analytical solution for the differential equation of the simple but nonlinear pendulum is derived. This solution is valid for any time and is not limited to any special initial instance or initial values. Moreover, this solution holds if the pendulum swings over or not. The method of approach is based on Jacobi elliptic functions…

Descriptors: Science Instruction, Equations (Mathematics), Motion, Mechanics (Physics)

Rodrigues, H.; de Pinho, M. O.; Portes, D., Jr.; Santiago, A. – European Journal of Physics, 2009

In continuation of a previous work, we present an analytic study of ascending vertical motion of a rocket subjected to a quadratic drag for the case where the mass-variation law is a linear function of time. We discuss the detailed analytical solution of the model differential equations in closed form. Examples of application are presented and…

Descriptors: Graduate Study, Undergraduate Study, College Science, Science Instruction

Belendez, A.; Alvarez, M. L.; Fernandez, E.; Pascual, I. – European Journal of Physics, 2009

A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for…

Descriptors: Mathematical Models, Educational Technology, Calculus, College Science

Low, Robert J. – European Journal of Physics, 2011

This paper gives a brief description of how Maxwell's equations are expressed in the language of differential forms and use this to provide an elegant demonstration of how the method of images (well known in electrostatics) also works for electrodynamics in the presence of an infinite plane conducting boundary. The paper should be accessible to an…

Descriptors: Graduate Students, Scientific Concepts, Equations (Mathematics), Undergraduate Students

Rojas-Trigos, J. B.; Bermejo-Arenas, J. A.; Marin, E. – European Journal of Physics, 2012

In this paper, some heat transfer characteristics through a sample that is uniformly heated on one of its surfaces by a power density modulated by a periodical square wave are discussed. The solution of this problem has two contributions, comprising a transient term and an oscillatory term, superposed to it. The analytical solution is compared to…

Descriptors: Research Methodology, Heat, Geometric Concepts, Comparative Analysis

Kinsler, Paul – European Journal of Physics, 2011

I explain a simple definition of causality in widespread use, and indicate how it links to the Kramers-Kronig relations. The specification of causality in terms of temporal differential equations then shows us the way to write down dynamical models so that their causal nature "in the sense used here" should be obvious to all. To extend existing…

Descriptors: Equations (Mathematics), Physics, Scientific Concepts, Models

Llibre, J; Teixeira, M. A. – European Journal of Physics, 2010

In a recent paper (Denny 2002 Eur. J. Phys. 23 449-58), entitled "The pendulum clock: a venerable dynamical system", Denny showed that in a first approximation the steady-state motion of a weight-driven pendulum clock is shown to be a stable limit cycle. He placed the problem in a historical context and obtained an approximate solution using the…

Descriptors: Calculus, Motion, Physics, Scientific Principles

Ferrario, Carlo; Passerini, Arianna – European Journal of Physics, 2007

In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…

Descriptors: Calculus, Science Instruction, Physics, Scientific Concepts

De Leon, Nelson; De Leon, Matthew N. – European Journal of Physics, 2007

We develop a two-dimensional flight simulator for lightweight (less than 10 g) indoor planes. The simulator consists of four coupled time differential equations describing the plane CG, plane pitch and motor. The equations are integrated numerically with appropriate parameters and initial conditions for two planes: (1) Science Olympiad and (2)…

Descriptors: Simulation, Aerospace Education, Equations (Mathematics), Science Instruction

Bringuier, E. – European Journal of Physics, 2011

This paper is an elementary introduction to particle diffusion in a medium where the coefficient of diffusion varies with position. The introduction is aimed at third-year university courses. We start from a simple model of particles hopping on a discrete lattice, in one or more dimensions, and then take the continuous-space limit so as to obtain…

Descriptors: Experiments, Calculus, College Curriculum, Higher Education

Johannessen, Kim – European Journal of Physics, 2011

An anharmonic solution to the differential equation describing the oscillations of a simple pendulum at large angles is discussed. The solution is expressed in terms of functions not involving the Jacobi elliptic functions. In the derivation, a sinusoidal expression, including a linear and a Fourier sine series in the argument, has been applied.…

Descriptors: Mathematics Education, Laboratory Equipment, Motion, Calculus

Tothova, Jana; Vasziova, Gabriela; Glod, Lukas; Lisy, Vladimir – European Journal of Physics, 2011

During the century from the publication of the work by Einstein (1905 "Ann. Phys." 17 549) Brownian motion has become an important paradigm in many fields of modern science. An essential impulse for the development of Brownian motion theory was given by the work of Langevin (1908 "C. R. Acad. Sci.", Paris 146 530), in which he proposed an…

Descriptors: Motion, Problem Solving, Science Instruction, Physics

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