arXiv subjects

Sylvio R Bistafa

Publications and source records attributed to Sylvio R Bistafa.

10 recordsLinked to original sources

arXiv2021

On the formation and propagation of pulses in ether

In 1746 Euler publishes E88 -- Nova theoria lucis et colorum (A new theory of light and colors) in five chapters. This is an annotated translation of Chapter II - De formatione ac propagatione pulsuum (On the formation and propagation of pulses in ether), in which Euler considers that the propagation of light in ether is similar to the propagation of sound in air. Based on the elastic properties of the air, he then tries to find the elastic properties of the ether, but, obviously, with no avail. Nonetheless, he correctly distinguished the local motion of the fluid particles from the motion of the pulse itself, and even attempted to estimate the speed of light.

physics.hist-ph↗

arXiv2021

Investigation of a water turbine built according to Euler's proposals (1754)

This is an annotated translation from German of Untersuchung einer nach den Euler'schen Vorschlagen (1754) gebauten Wasserturbine [Investigation of a water turbine built according to Euler's proposals (1754)] that reports the tests results of a modern (1944) prototype of the so-called Segner-Euler turbine, which was strictly constructed according to Euler's prescription as laid down in E222 -- Theorie plus complete des machines qui sont mises en mouvement par la reaction de l'eau. (Memoires de l'academie des sciences de Berlin 1756, Vol. 10, pp. 227-295.), showing the feasibility of Euler's original proposal. A reproduction of the original paper is attached at the end of the translation.

physics.hist-ph↗

arXiv2021

An English translation of L. Euler's "Calculations on aerostatic balloons made by the late Mr. Leonhard Euler, as they were found on his blackboard, after his death on 7 September 1783"

This is an English translation of E579 in which the introductory remarks are in French, while Euler's original text is in Latin. By considering the balance of forces acting on a raising balloon on an isothermal atmosphere, namely the weight of the balloon, the buoyant force, and the aerodynamic drag force, Euler provides closed formulas for the calculation of the maximum altitude reached by the balloon, the altitude for which the velocity is maximum, the maximum velocity attained by the balloon, and the total ascending time.

physics.hist-ph↗

arXiv2021

A translation of G.W. Krafft's "On a new class of oscillations"

This is a translation from Latin of 'De novo oscillationum genere', which was motivated by Krafft's accidental observation of a suspended clock setting itself in constant motion as a pendulum. This publication, in turn, motivated Euler to write 'De novo genere oscillationum', in which Euler derived for the first time, the differential equation for the (undamped) simple harmonic oscillator under harmonic excitation.

physics.hist-ph↗

arXiv2021

A translation of L. Euler's "On a new class of oscillations"

This is an annotated translation of E126 'De novo genere oscillationum', in which Euler derived for the first time, the differential equation of the (undamped) simple harmonic oscillator under harmonic excitation, namely, the motion of an object subjected to two acting forces, one proportional to the distance travelled, the other one varying sinusoidally with time. He then developed a general solution, making extensive use direct and inverse sine and cosine functions. After much manipulation of the resulting equations, he proceeds to analyze the periodicity of the solutions by varying the values of the parameters, to finally find out the phenomenon of resonance by saying "... Among all these cases, the one which deserves particular attention is that for which 2b=a, in which the oscillation distance eventually grows up to infinite: this effect is most remarkable, since it is generated by finite forces."

physics.hist-ph↗

arXiv2021

A translation of L. Euler's "On the motion of comets in parabolic orbits, having the Sun in the focus"

This is a translation from Latin of E840 'De motu cometarum in orbitis parabolicis, solem in foco habentibus', in which Euler addresses six problems related to comets in heliocentric parabolic orbits. Problem 1: Find the true anomaly of a heliocentric comet from the latus rectum of the orbit and the medium Earth to Sun distance. Problem 2: Find the orbit of a heliocentric comet from three given positions. Problem 3: Knowing the orbit of a comet, and the instant in time in which it dwells in the perihelion, define its longitude and latitude at any time. Problem 4: From two locations of a heliocentric comet, find the inclination of the comet's orbit in relation to the ecliptic, and the positions of the nodes. Problem 5: From the time before or after the comet had reached the perihelion, and from the comet's distance to the perihelion as seen from the Sun, find the same distance in another time before or after it had appeared in the perihelion. Problem 6: Find the orbit of a comet from three given heliocentric longitudes and latitudes. From these problems, several corollaries and scholia are derived.

physics.hist-ph↗

arXiv2021

A translation of L. Euler's "An easy method for calculating the motion of celestial bodies perturbed in any manner avoiding astronomical computations"

This is a translation from Latin of E348 'Methodus facilis motus corporum coelestium utcunque perturbatos ad rationem calculi astronomici revocandi', in which Euler develops a method to alleviate the astronomical computations in a typical celestial three-body problem represented by Sun, Earth and Moon. In this work, Euler's approach consists of two parts: geometrical and mechanical. The geometrical part contains most of the analytical developments, in which Euler makes use of Cartesian and spherical trigonometry as well - the latter not always in a clear enough way. With few sketches to show the geometrical constructions envisaged by Euler - represented by several geometrical variables -, it is a hard to follow publication. The Translator, on trying to clear the way to the non-specialized reader, used the best of his abilities to add his own figures to the translation. In the latter part of the work, Euler particularizes his developments to the Moon, ending up with eight coupled differential equations for resolving the perturbed motion of this celestial body, which makes his claim of an "easy method" as being rather fallacious. Despite showing great analytical skills, Euler did not give indications on how this system of equations could be solved, which renders his efforts practically useless in the determination of the variations of the nodal line and inclination of the Moon's orbit.

physics.hist-ph↗

arXiv2021

A translation of L. Euler's "On the rectilinear motion of three bodies mutually attracting each other"

This is an annotated translation from Latin of E327 'De motu rectilineo trium corporum se mutuo attrahentium'. In this publication, Euler considers three bodies lying on a straight line, which are attracted to each other by central forces inversely proportional to the square of their separation distance (inverse-square law). Although not explicitly mentioned by Euler, this is an exact solution of three bodies that move around the common center of mass and always line up. The solution given by Euler could represent a hypothetical situation of Sun, Earth and Moon in perpetual alignment in syzygy, for which the parameter that controls the distances among the planets was found to be given by a quintic function.

physics.hist-ph↗

arXiv2021

A translation of L. Euler's "Simple determination of the orbit of a comet, when it is possible to observe its passage across the ecliptic twice"

This is the translation from Latin of E547 'Determinatio facilis orbitae cometae, cuius transitum per eclipticam bis observare licuit', in which Euler addresses the determination of a comet's parabolic orbit, with the Sun at the focus, from two astronomical observations from the earth, when the comet crosses the ecliptic at the ascending and descending nodes. The key point of the calculation is the solution of a fourth degree polynomial, from which the determination of the orbital parameters are determined from one of its roots.

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arXiv2021

A translation of L. Euler's "Considerations on the motion of celestial bodies"

Euler wrote several papers on Astronomy, most of them in Latin. This is a commented translation of E304 'Considerationes de motu corporum coelestium' (Considerations on the motion of celestial bodies). In this publication, Euler essentially focuses on the solution of two particular motions of a three-body problem consisting of Sun, Earth and Moon. The first motion, represents a hypothetical situation of these three celestial bodies in perpetual alignment in syzygy - the three-body problem on a straight line -, for which the parameter that controls the distances among the planets was found to be given by a quintic function. The conclusion was that if the Moon were four times more distant from the Earth (either in conjunction or in opposition), a motion of this kind would have been possible to exist, such that the Moon would appear always connected to the Sun. The second motion considered by Euler was Moon libration, when these planets are aligned in regular syzygy. Here, perhaps for the first time, Euler introduces an archaic form of a Fourier sine series expansion to describe the Moon's wagging motion. However, as Euler himself recognizes, the calculations turned out very tedious, and led him to greatly simplify his model in order to obtain some numerical values for the phenomenon.

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