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Kepler's laws are an appropriate topic to highlight the significance of the pedal equation in physics. There are several articles that obtain Kepler's laws through conservation and gravitation laws. This can be shown more easily and ingeniously if one uses the pedal equation of an ellipse. In fact, the complete kinematics of a particle in an attractive central force field can be derived from one single pedal form. Though many articles use the pedal equation, the classical procedure (without proof) for obtaining the pedal equation is mentioned only in a few because the classical derivations can sometimes be lengthier and are not simple. In this paper, using elementary physics, we derive the pedal equation for all conic sections in a unique, short, and pedagogical way. Later, from the dynamics of a particle in the attractive central force field, we deduce the single pedal form, which elegantly describes all the possible trajectories. Also, for the purpose of completeness, we derive Kepler's laws. Key words: pin and string construction of conics, pedal equation, central force field, conservation laws, trajectories and Kepler laws. Les lois de Kepler constituent un sujet approprie pour faire ressortir la pertinence de l'equation podaire en physique. Il y a plusieurs articles qui obtiennent les lois de Kepler comme consequence de lois de conservation et de gravite. Ce resultat peut s'obtenir de facon plus facile et plus ingenieuse en utilisant l'equation podaire de l'ellipse. En fait, la cinematique complete d'une particule dans un champ de force central peut etre obtenue d'une simple formule podaire. Meme si bon nombre d'articles utilisent l'equation podaire, seulement quelques uns presentent la procedure classique pour obtenir (sans preuve) l'equation podaire. La raison est probablement que cette procedure est longue et pas simple. Notre but ici est d'utiliser des arguments physiques simples pour obtenir l'equation podaire pour toutes les sections coniques d'une facon courte, simple et pedagogique. Par la suite, a partir de la dynamique de la particule dans le champ de force central, nous deduisons la forme podaire simple qui decrit de facon elegante toutes les trajectoires possibles. Pour etre plus complets, nous obtenons ensuite les lois de Kepler. [Traduit par la Redaction] Mots-cles : construction de coniques a l'aide de punaises et de cordelettes, equation podaire, champ de force central, lois de conservation, trajectoires et lois de Kepler., 1. Introduction The accurate observations of Tycho Brahe and the discovery of the three laws by Johannes Kepler using them, can be considered the epitome of observational science. Kepler, after [...]

We quantitatively investigate the axial imaging properties of dynamic phase-contrast microscopy, with a special focus on typical combinations of tracer particles and magnifications that are used for velocimetry analysis. We show, for the first time, that a dynamic phase-contrast microscope, which is the integration of an all-optical novelty filter in a commercially available inverted microscope, can visualize three-dimensional velocity fields with a significantly reduced optical sectioning depth. The depth of field for dynamic phase-contrast microscopy is extracted from the three-dimensional response function and compared with the respective values for incoherent bright-field illumination. These results are then used to perform a depth-resolved particle image velocimetry analysis of Hagen-Poiseuille as well as electro-osmotically actuated flows in a microchannel. OCIS codes: 110.0180, 180.4315, 180.6900, 190.7070.

A fast computation algorithm for fine-pixel aerial images is presented that modifies the transmission cross coefficient approach of Hopkins as a product of two matrices. The spatial frequency of the image is calculated by the sum of diagonal and off-diagonal elements of the matrix. Let N, [N.sub.F], and M be the number of the point sources, the sampling number for fast Fourier transform, and the sampling number in the spatial frequency domain ranging twice the pupil size, respectively. The calculation time of this method is proportional to BN[[(M- 1)/2].sup.4], while that of a conventional source integration method is [2ANN.sub.F][log.sub.2] [N.sub.F], where A and B are constants and generally B < A If [N.sub.F] is sufficiently greater than M or M is small enough, which is the fine-pixel condition, this method runs faster than the source integration method. If the coherence factor is 0.9 and M [less than or equal to] 55, this method runs faster than the source integration even under the Nyquist sampling condition. OCIS codes: 110.4980, 110.5220, 110.2990.

The classical Abraham-Lorentz formula for the radiation reaction on a point charge suffers from two notorious defects: runaways and preacceleration. Recently, several authors have advocated as an alternative the Landau-Lifshitz formula, which has neither fault. The latter formula is often presented as an approximation to Abraham-Lorentz, raising the delicate question of how an approximation can be considered more accurate than the original. For a spherical shell of finite size, the equation for the radiation reaction is noncontroversial. We begin there, obtain the Abraham-Lorentz and Landau-Lifshitz expressions as limiting cases, and undertake some numerical studies to determine which is superior. [c] 2010 American Association of Physics Teachers. [DOI: 10.1119/1.3269900]

Equations for Rayleigh scattering in a mixture of gases are derived and compared to frequent approximations in the literature. The traditional Rayleigh scattering equation as modified by King for scatter from a pure gas is correct, whereas another version sometimes appearing in modern literature is erroneous. Use of a mixture's refractive index, which is equivalent to assuming the isotropic molecular polarizabilities of the component gases are identical, is an approximation. Another common approximation is using only number-density weighting of the King factors. Approximation errors can be large when the major components of a mixture have disparate optical properties. Fortunately, the errors for Earth's air are much smaller and comparable to errors from other sources. OCIS codes: 290.5870, 290.1310, 010.1320, 280.3640.

We present a method for orientation-selective edge detection and enhancement based on the irradiance transport equation. The proposed technique distinguishes the sign of the derivative of the intensity pattern along an arbitrarily selected direction. The method is based on the capacity of liquid-crystal displays to generate simultaneously a contrast reverted replica of the image displayed on it. When both images (the original one and its replica) are imagined across a slightly defocused plane, one obtains an image with enhanced first derivatives. Unlike most Fourier methods, the proposed technique works well with a low-coherence light source, and it does not require precise alignment. The proposed method does not involve numerical processing, and thus it could be potentially useful for processing large images in real-time applications. Validation experiments are presented. [c] 2010 Optical Society of America OCIS codes: 100.2980, 100.2810.

The propagation of a dispersive shock wave is studied in a quintic-derivative nonlinear Schrodinger (Q-DNLS) equation, which may describe, Por example, the wave propagation on a discrete electrical transmission line. II is shown that a physical system described by a Q-DNLS equation without a dissipative term may support the propagation of shock waves. The influence of the derivative nonlinearity terms on the shock is analyzed. Using the round exact shock solutions of the Q-DNLS equation as the initial input signal, we investigate numerically the spatiotemporal stability of the shock signal in the network. PACS Nos: 42.65.Tg, 42.25.Bs, 84.40.Az, 02.60.Cb Nous etudions la propagation d'une onde de choc dispersive a l'aide d'une equation differentielle quintique non lineaire de Schrodinger (equation Q-DNLS), qui peut decrire, par exemple. la propagation d'onde sur une ligne de transmission electrique discrete. Nous montrons qu'un systeme physique decrit par une equation Q-DNLS sans terme dissipatif peut permettre la propagation d'onde de choc. Nous etudions l'influence des termes non lineaires en derivee sur l'onde de choc. Utilisant comme signal de depart, la solution exacte pour l'onde de choc obtenue de l'equation Q-DNLS, nous etudions la stabilite spatiotemporelle du signal de choc dans la ligne. [Traduit par la Redaction], 1. Introduction Since the pioneering works by Hirota and Suzuky [l] on electrical transmission lines simulating the Toda lattice, a growing interest has been devoted to the use of the [...]

We show how the Proca equations can be deduced from first principles in a way that is similar to the derivations of the Dirac relativistic electron equation and Maxwell equations. [DOI: 10.1119/1.3137042]

An alternative derivation of the first-order relativistic contribution to perihelic precession is presented. Orbital motion in the Schwarzschild geometry is considered in the Keplerian limit, and the orbit equation is derived for approximate elliptical motion. The method of solution makes use of coordinate transformations and the correspondence principle rather than the standard perturbative approach. The form of the resulting orbit equation is similar to that derived from Newtonian mechanics and includes first-order corrections to Kepler's orbits due to general relativity. The associated relativistic contribution to perihelic precession agrees with established first-order results. The reduced radius for the circular orbit is in agreement to first-order with that calculated from the Schwarzschild effective potential. The method of solution is understandable by undergraduate students. [DOI: 10.1119/1.3159611]

The exact solutions of the Duffin-Kemmer-Petiau (DKP) oscillator for spin-0 particles have been studied in noncommutative phase space. The results show that due to the noncommutative effect, the energy spectrum of the DKP oscillator for spin-0 particles is no longer degenerate. In addition, we obtain the nonrelativistic limit of the energy spectrum. PACS Nos: 02.40.Gh, 03.65.-w, 03.65.Ge, 03.65.Pm Nous avons etudie sur un espace de phase non commutatif les solutions exactes de l'oscillateur Duffin-Kemmer-Petiau (DKP) pour des particules de spin zero. Les resultats montrent qu'a cause de la non commutativite, le spectre d'energie de particules massives de spin nul dans le potentiel d'oscillateur de Dirac n'est pas degenere. Nous obtenons aussi la limite non relativiste du spectre d'energie. [Traduit par la Redaction], 1. Introduction It is well known that the Duffin-Kemmer-Petiau (DKP) equation is a first-order relativistic wave equation for spin 0 and 1 bosons [1-3], which describes some problems in nuclear [...]

The Klein-Gordon equation in the presence of a spatially one-dimensional Hulthen potential is solved exactly and the scattering solutions are obtained in terms of hypergeometric functions. The transmission coefficient is derived by the matching conditions on the wave functions and the conditions for the existence of transmission resonances are investigated. It is shown how the zero-reflection condition depends on the shape of the potential. PACS Nos: 03.65.Nk, 03.65.Pm Nous solutionnons exactement l'equation de Klein-Gordon en 1+1 D avec un potentiel a une dimension spatiale de Hulthen et nous obtenons les solutions de diffusion sous la forme de fonctions hypergeometriques. Le coefficient de transmission est obtenu en mariant les conditions sur les fonctions d'onde et nous etudions les conditions d'existence d'une transmission resonante. Nous montrons que la condition de reflexion nulle depend de la forme du potentiel. [Traduit par la Redaction], The study of low-momentum scattering in the Schrodinger equation in one-dimensional even potentials shows that, as momentum goes to zero, the reflection coefficient goes to unity unless the potential V(x) [...]

Quantum decoherence is a proposed mechanism for the emergence of classical physics from the quantum mechanics. It has been developed extensively in recent years, but is sufficiently technically complicated to discourage widespread understanding. In this paper we provide a gentle introduction to quantum decoherence. We introduce state operators and their density matrix representations to describe composite systems, such as an experiment and its environment. We illustrate how the loss of information about a subsystem can cause a quantum system to appear classical. We first analyze a discrete example of phase randomization, then a Bell state, and finally a continuous system. In the final case we provide an accessible derivation of a major early result of decoherence theory, the master equation of quantum Brownian motion. We conclude by applying the master equation to the decoherence of a simple harmonic oscillator, with results reminiscent of our earlier discrete examples.

We show how to obtain the first multipole contributions to the electromagnetic radiation emitted by an arbitrary localized source directly from the Jefimenko equation for the magnetic field and the Panofsky-Phillips equation for the electric field. This procedure avoids the unnecessary calculation of the electromagnetic potentials. [DOI: 10.1119/1.2990666]

Bertrand's theorem is formulated as the solution of an inverse problem for classical one-dimensional motion. We show that the solutions of this problem, if suitably restricted, can be obtained by solving an elementary equation. This approach provides a compact and elegant proof of Bertrand's theorem.

In the preceding article we argue that biquaternionic extension of Klein-Gordon equation has solution containing imaginary part, which differs appreciably from known solution of KGE. In the present article we [...]