DOCSLIB.ORG

1 Portraits Leonhard Euler Daniel Bernoulli Johann-Heinrich Lambert

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
1 Portraits Leonhard Euler Daniel Bernoulli Johann-Heinrich Lambert Portraits Leonhard Euler Daniel Bernoulli Johann-Heinrich Lambert Compiled and translated by Oscar Sheynin Berlin, 2010 Copyright Sheynin 2010 www.sheynin.de ISBN 3-938417-01-3 1 Contents Foreword I. Nicolaus Fuss, Eulogy on Leonhard Euler, 1786. Translated from German II. M. J. A. N. Condorcet, Eulogy on Euler, 1786. Translated from French III. Daniel Bernoulli, Autobiography. Translated from Russian; Latin original received in Petersburg in 1776 IV. M. J. A. N. Condorcet, Eulogy on [Daniel] Bernoulli, 1785. In French. Translated by Daniel II Bernoulli in German, 1787. This translation considers both versions V. R. Wolf, Daniel Bernoulli from Basel, 1700 – 1782, 1860. Translated from German VI. Gleb K. Michajlov, The Life and Work of Daniel Bernoullli, 2005. Translated from German VII. Daniel Bernoulli, List of Contributions, 2002 VIII. J. H. S. Formey, Eulogy on Lambert, 1780. Translated from French IX. R. Wolf, Joh. Heinrich Lambert from Mühlhausen, 1728 – 1777, 1860. Translated from German X. J.-H. Lambert, List of Publications, 1970 XI. Oscar Sheynin, Supplement: Daniel Bernoulli’s Instructions for Meteorological Stations 2 Foreword Along with the main eulogies and biographies [i, ii, iv, v, viii, ix], I have included a recent biography of Daniel Bernoulli [vi], his autobiography [iii], for the first time translated from the Russian translation of the Latin original but regrettably incomplete, and lists of published works by Daniel Bernoulli [vii] and Lambert [x]. The first of these lists is readily available, but there are so many references to the works of these scientists in the main texts, that I had no other reasonable alternative. A very short Supplement [xi] provides notice of instructions on geophysical observations compiled by Daniel Bernoulli. The older eulogies and biographies are certainly dated and sometimes contradict each other; in such cases, however, it is easy to discover the truth and in any case they provide valuable information about the life of their heroes and the attitude of the contemporaries to them. I have separated each contribution into sections which at the very least ensures the possibility of referring to their texts more definitely. The references such as [1736/15] show the year of publication and the number of the book or memoir in the lists of publications of Daniel Bernoulli or Lambert. For Euler, the notation is similar, but the number of publication is that given by Eneström (1910/1913) as reprinted in Euler (1962, pp. 352 – 385), see Joint Bibliography to [i] and [ii]. The Notes to each contribution are initialled by the appropriate author or by me. The initial F. R. in the Notes to [i] stand for Ferdinand Rudio, the Editor of the appropriate volume of Euler’s Opera omnia . The references to sources mentioned below in my Foreword are included in the Bibliographies to the appropriate contributions. A year ago I have published a collection of almost the same contributions translated into Russian. Now I see that it contains some mistakes, and the only explanation (not an excuse) seems to be that I have somehow failed to check my first draft. General Comments on Separate Contributions Comments on [i] The original French text of the Eulogy was published separately, then reprinted in the Nova Acta Acad. Scient. Imp. Petropolitana , 1787, pp. 159 – 212. Its German translation by the author himself was subdivided into sections separated by intervals; instead, I numbered them. Professor Gautschi had kindly sent me a draft of his own translation of the German text but avoided further contacts. Consequently, I have only made use of his work for checking here and there my own work and I also inserted his own translation of a Latin passage in § 29. In his Introduction, Fuss mentions von Michel, who allowed “Euler’s life to appear in a native guise by means of his art”. Rudio (p. XL of Euler’s Opera omnia , ser. 1, t. 1) explains that the German translation of the Eulogy was published in Basel at the expense of the 3 state (of Switzerland) and “adorned” by Euler’s portrait copying an engraving by Christian von Mechel (reproduced after the title page in that volume). Nikolai Ivanovich Fuss (1755 – 1826) was Euler’s disciple and became a member of the Petersburg Academy. He is known by his work in geometry, but mainly as Euler’s “small satellite” (Youshkevich 1968, p. 196). For a description of his life and work see Lysenko (1975). Two shortcomings of his Eulogy are, first, that he referred to the memoirs of his teacher not definitely enough; and, second, that he obviously prettified Friedrich II. Here is what Youshkevich (1968, p. 108) had to say about that monarch: Euler and Friedrich II “much disagreed about everything”, mathematics in particular. The monarch “did not appreciate any abstract investigations” and “all the time interfered” in the management of the Berlin Academy. Finally, with the best intentions Fuss invariably called Euler a genius and a great man, but, as far as style goes, he had thus overdone his admiration. Literature about Euler is of course immense. Among the newest sources I mention, Du Pasquier (1927), Spieß (1929), Michajlov (1985), Fellmann (2007) and of course Truesdell (in particular, his appropriate essays in vols. 11 and 12 of Euler’s Opera omnia , ser. 2). Many more worthy publications about Euler are appearing/will yet appear in connection with his jubilee. Comments on [ii] Condorcet provides some interesting details about Euler, but, taken as a whole, his Eloge is simply inadequate and shows disrespect to its readers. Repetitions abound, the description of Euler’s life and work is superficial, in places difficult to understand, sometimes illogical, in other places difficult if at all possible to understand, and ends (§ 38) with an astonishing statement to the effect that Euler’s life was almost cloudless. I have substantiated all this in my Notes which follow Condorcet’s text. Then, a few alleged facts contradict Fuss who undoubtedly knew everything relevant incomparably better. I have translated this Eloge and thus hopefully done away with Condorcet as an authority on Euler but I ought to add that France, one of the most enlightened European nation, as Condorcet reasonably believed, very soon found itself in the turmoil of a bloody revolution and he himself committed suicide while in detention. Comments on [iii] Here is what is known about Daniel Bernoulli’s Autobiography (Smirnov 1959, p. 501): it is A translation [into Russian] of a Latin Autobiography of Daniel Bernoulli kept at the Archive of the Academy of Sciences of the USSR. The Petersburg Academy of Sciences received it on 21 July 1776. Its ending is apparently lost . Smirnov did not name the translator, likely Gokhman, who translated the entire Hydrodynamica , and in any case, according to its style the Russian text could not have been written earlier than in the 1920s or 1930s. 4 The translator had inserted in brackets a few Latin words from the original text. Bernoulli had sent his Autobiography to Petersburg and likely therefore somewhat prettified his relations with the Imperial Academy. Comments on [iv] and [v] Daniel Bernoulli (1700 – 1782) was a most prominent scientist mainly known for his pioneer work in mechanics and physics; see Straub (1970) for a modern description of his life and work. The first Eulogy [iv] is superficial (§§ 11 – 13), difficult to understand (§ 5 and description of works in mechanics), partly wrong (Daniel Bernoulli had not been happy and healthy all his life, see Wolf [v]) and includes long passages not directly bearing on his subject whereas his § 17 is as good as incoherent twaddle, cf. Note 19. I have checked his text against its German translation by Daniel II Bernoulli and in many places followed him rather than Condorcet but he obviously did not know as much as Wolf [v] about the life of his uncle. I note that he called D. B. our Daniel and our Bernoulli and manifested excessive respect for Condorcet. I am grateful to Dr. Fritz Nagel Basel) who sent me a photostat copy of that translation. Wolf (1858 – 1862) fulfilled a great work on the history of science in Switzerland and in particular provided much information on the Bernoulli family and on scientists more or less connected with Daniel Bernoulli including many passages from their correspondence with each other and him. Regrettably, he [v] documented his sources quite insufficiently and I was often unable to improve the situation. And he also felt himself at liberty to leave his sentences poorly connected with each other which sometimes hinders understanding (and translation). I left out many passages concerning other scientists. Some of his phrases are italicized or spaced out but it remains unclear whether by Wolf himself or by the authors whom he quotes. Neither Condorcet, nor Wolf (nor Daniel II Bernoulli) were able to describe satisfactorily Daniel Bernoulli’s work in statistics. On this subject see Todhunter (1865), Sheynin (1972) and Hald (1998). Comments on [viii] and [ix] Lambert is known less than Euler or Daniel Bernoulli; his modern biographer is Scriba (1973). Concerning the eulogies on him, I note that Formey [viii] compiled it as a philosopher or historian and Wolf [ix], as an astronomer, but did not notice Lambert’s pioneer work on the theory of errors (Sheynin 1971). In addition, Wolf mentioned hardly known Swiss place-names which I was unable to identify. I 5 Nicolaus Fuss Eulogy on Leonhard Euler Translated from French and extended by various additions by the author himself. Basel, 1786
Load more

Recommended publications
  • The Icha Newsletter Newsletter of the Inter-Union Commission For
    International Astronomical Union International Union of the History and Philosophy of Science DHS/IUHPS ______________________________________________________________________________________________________________________ THE ICHA NEWSLETTER NEWSLETTER OF THE INTER-UNION COMMISSION FOR HISTORY OF ASTRONOMY* ____________________________________________________________ __________________________________________________________ No. 11 – January 2011 SUMMARY A. Archaeoastronomy and Ethnoastronomy: Building Bridges between Cultures – IAU Symposium S278 Report by C. Ruggles ..................................................... 1 B. Historical Observatory building to be restored by A. Simpson …..…..…...… 5 C. History of Astronomy in India by B. S. Shylaja ……………………………….. 6 D. Journals and Publications: - Acta Historica Astronomiae by Hilmar W. Duerbeck ................................ 8 Books 2008/2011 ............................................................................................. 9 Some research papers by C41/ICHA members - 2009/2010 ........................... 9 E. News - Exhibitions on the Antikythera Mechanism by E. Nicolaidis ……………. 10 - XII Universeum Meeting by M. Lourenço, S. Talas, R. Wittje ………….. 10 - XXX Scientific Instrument Symposium by K.Gaulke ..………………… 12 F. ICHA Member News by B. Corbin ………………………………………… 13 * The ICHA includes IAU Commission 41 (History of Astronomy), all of whose members are, ipso facto, members of the ICHA. ________________________________________________________________________________________________________________________
    [Show full text]
  • The First Measurement of the Deflection of the Vertical in Longitude
    Eur. Phys. J. H. DOI: 10.1140/epjh/e2014-40055-2 The first measurement of the deflection of the vertical in longitude The figure of the earth in the early 19th century Andreas Schrimpfa Philipps-Universit¨atMarburg, Fachbereich Physik, Renthof 5, D-35032 Marburg, Germany Abstract. During the summer of 1837 Christian Ludwig Gerling, a for- mer student of Carl Friedrich Gauß’s, organized the world wide first de- termination of the deflection of the vertical in longitude. From a mobile observatory at the Frauenberg near Marburg (Hesse) he measured the astronomical longitude difference between C.F. Gauß’s observatory at G¨ottingenand F.G.B. Nicolai's observatory at Mannheim within an er- ror of 000: 4. To achieve this precision he first used a series of light signals for synchronizing the observatory clocks and, second, he very carefully corrected for the varying reaction time of the observers. By comparing these astronomical results with the geodetic{determined longitude dif- ferences he had recently measured for the triangulation of Kurhessen, he was able to extract a combined value of the deflection of the vertical in longitude of G¨ottingenand Mannheim. His results closely agree with modern vertical deflection data. 1 Introduction The discussion about the figure of the earth and its determination was an open ques- tion for almost two thousand years, the sciences involved were geodesy, geography and astronomy. Without precise instruments the everyday experience suggested a flat, plane world, although ideas of a spherically shaped earth were known and ac- cepted even in the ancient world. Assuming that the easily observable daily motion of the stars is due to the rotation of the earth, the rotational axis can be used to define a celestial sphere; a coordinate system, where the stars' position is given by two angles.
    [Show full text]
  • Staircase of Vienna Observatory (Institut Für Astronomie Der Universität Wien)
    Figure 15.1: Staircase of Vienna Observatory (Institut für Astronomie der Universität Wien) 142 15. The University Observatory Vienna Anneliese Schnell (Vienna, Austria) 15.1 Introduction should prefer non-German instrument makers (E. Weiss 1873). In spring of 2008 the new Vienna Observatory was th commemorating its 125 anniversary, it was officially During a couple of years Vienna Observatory was edit- opened by Emperor Franz Joseph in 1883. Regular ob- ing an astronomical calendar. In the 1874 edition K. L. servations had started in 1880. Viennese astronomers Littrow wrote a contribution about the new observatory had planned that observatory for a long time. Already th in which he defined the instrumental needs: Karl von Littrow’s father had plans early in the 19 “für Topographie des Himmels ein mächtiges parallakti- century (at that time according to a letter from Joseph sches Fernrohr, ein dioptrisches Instrument von 25 Zoll Johann Littrow to Gauß from December 1, 1823 the Öffnung. Da sich aber ein Werkzeug von solcher Grö- observatory of Turku was taken as model) (Reich 2008), ße für laufende Beobachtungen (Ortsbestimmung neu- but it lasted until 1867 when it was decided to build a er Planeten und Kometen, fortgesetzte Doppelsternmes- new main building of the university of Vienna and also sungen, etc.) nicht eignet, ein zweites, kleineres, daher a new observatory. Viennese astronomers at that time leichter zu handhabendes, aber zur Beobachtung licht- had an excellent training in mathematics, they mostly schwacher Objekte immer noch hinreichendes Teleskop worked on positional astronomy and celestial mechanics. von etwa 10 Zoll Öffnung, und ein Meridiankreis er- They believed in F.
    [Show full text]
  • Ice& Stone 2020
    Ice & Stone 2020 WEEK 33: AUGUST 9-15 Presented by The Earthrise Institute # 33 Authored by Alan Hale About Ice And Stone 2020 It is my pleasure to welcome all educators, students, topics include: main-belt asteroids, near-Earth asteroids, and anybody else who might be interested, to Ice and “Great Comets,” spacecraft visits (both past and Stone 2020. This is an educational package I have put future), meteorites, and “small bodies” in popular together to cover the so-called “small bodies” of the literature and music. solar system, which in general means asteroids and comets, although this also includes the small moons of Throughout 2020 there will be various comets that are the various planets as well as meteors, meteorites, and visible in our skies and various asteroids passing by Earth interplanetary dust. Although these objects may be -- some of which are already known, some of which “small” compared to the planets of our solar system, will be discovered “in the act” -- and there will also be they are nevertheless of high interest and importance various asteroids of the main asteroid belt that are visible for several reasons, including: as well as “occultations” of stars by various asteroids visible from certain locations on Earth’s surface. Ice a) they are believed to be the “leftovers” from the and Stone 2020 will make note of these occasions and formation of the solar system, so studying them provides appearances as they take place. The “Comet Resource valuable insights into our origins, including Earth and of Center” at the Earthrise web site contains information life on Earth, including ourselves; about the brighter comets that are visible in the sky at any given time and, for those who are interested, I will b) we have learned that this process isn’t over yet, and also occasionally share information about the goings-on that there are still objects out there that can impact in my life as I observe these comets.
    [Show full text]
  • New General Principle of Mechanics and Its Application to General Nonideal Nonholonomic Systems
    New General Principle of Mechanics and Its Application to General Nonideal Nonholonomic Systems Firdaus E. Udwadia1 Abstract: In this paper we develop a general minimum principle of analytical dynamics that is applicable to nonideal constraints. The new principle encompasses Gauss’s Principle of Least Constraint. We use this principle to obtain the general, explicit, equations of motion for holonomically and/or nonholonomically constrained systems with non-ideal constraints. Examples of a nonholonomically constrained system where the constraints are nonideal, and of a system with sliding friction, are presented. DOI: 10.1061/͑ASCE͒0733-9399͑2005͒131:4͑444͒ CE Database subject headings: Constraints; Equations of motion; Mechanical systems; Friction. Introduction ments. Such systems have, to date, been left outside the perview of the Lagrangian framework. As stated by Goldstein ͑1981, p. The motion of complex mechanical systems is often mathemati- 14͒ “This ͓total work done by forces of constraint equal to zero͔ cally modeled by what we call their equations of motion. Several is no longer true if sliding friction is present, and we must exclude formalisms ͓Lagrange’s equations ͑Lagrange 1787͒, Gibbs– such systems from our ͓Lagrangian͔ formulation.” And Pars Appell equations ͑Gibbs 1879, Appell 1899͒, generalized inverse ͑1979͒ in his treatise on analytical dynamics writes, “There are in equations ͑Udwadia and Kalaba 1992͔͒ have been developed for fact systems for which the principle enunciated ͓D’Alembert’s obtaining the equations of motion for such structural and me- principle͔… does not hold. But such systems will not be consid- chanical systems. Though these formalisms do not all afford the ered in this book.” Newtonian approaches are usually used to deal same ease of use in any given practical situation, they are equiva- with the problem of sliding friction ͑Goldstein 1981͒.
    [Show full text]
  • On Stability Problem of a Top Rendiconti Del Seminario Matematico Della Università Di Padova, Tome 68 (1982), P
    RENDICONTI del SEMINARIO MATEMATICO della UNIVERSITÀ DI PADOVA V. V. RUMJANTSEV On stability problem of a top Rendiconti del Seminario Matematico della Università di Padova, tome 68 (1982), p. 119-128 <http://www.numdam.org/item?id=RSMUP_1982__68__119_0> © Rendiconti del Seminario Matematico della Università di Padova, 1982, tous droits réservés. L’accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova » (http://rendiconti.math.unipd.it/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit conte- nir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ On Stability Problem of a Top. V. V. RUMJANTSEV (*) This paper deals with the stability of a heavy gyrostate [1] on a horizontal plane. The gyrostate is considered as a rigid body with a rotor rotating freely (without friction) about an axis invariably con- nected with the body leaning on a plane by a convex surface, i.e. the top in a broad sence of this word. For mechanician the top is a symple and principal object of study [2] attracting investigators’ attention. 1. Let $ql be the fixed coordinate system with the origin in some point of a horizontal plane and vertically up directed axis I with unit vector y; OXIX2Xa is the coordinate system rigidly connected with the body with the origin in centre of mass of gyrostate and axis ~3 coincided with one of its principal central axes of inertia.
    [Show full text]
  • Friedrich Zöllner's Correspondence with Wilhelm Foerster
    See discussions, stats, and author profiles for this publication at: http://www.researchgate.net/publication/241504525 Friedrich Zöllner's correspondence with Wilhelm Foerster CHAPTER · JANUARY 2000 CITATION READS 1 8 2 AUTHORS, INCLUDING: Wolfgang R. Dick Federal Agency for Cartography and Geodesy 283 PUBLICATIONS 192 CITATIONS SEE PROFILE Available from: Wolfgang R. Dick Retrieved on: 14 October 2015 11 Friedrich Z¨ollner’s correspondence with Wilhelm Foerster Wolfgang R. Dick Otterkiez 14 D-14478 Potsdam Federal Republic of Germany Gisela M¨unzel Fockestrasse 43 D-04275 Leipzig Federal Republic of Germany Abstract Thirty one letters by Karl Friedrich Z¨ollner to Wilhelm Foerster have sur- vived, being probably nearly all that have been written by Z¨ollner. Most of Foerster’s letters have been lost, with the exception of one preserved in original and some published (at least in parts) in 1899. An overview of the relations of Z¨ollner and Foerster and of their correspondence is given, and some quotes from Z¨ollner’s letters are presented. These give new insights into Z¨ollner’s scientific and private life. 11.1 Z¨ollner’s friend and correspondent Wilhelm Foerster Wilhelm Foerster was born on December 16, 1832 in the Silesian town of Gr¨unberg, so that he was almost two years older than Z¨ollner. His way into 121 122 ZOLLNER’S¨ CORRESPONDENCE WITH FOERSTER astronomy was more rapid and straight in comparison to Z¨ollner’s. Foerster studied first at Berlin, but after three semesters he left for Bonn, where — under the direction of Argelander — he graduated with a dissertation on the geographical latitude of Bonn Observatory.
    [Show full text]
  • On the Foundations of Analytical Dynamics F.E
    International Journal of Non-Linear Mechanics 37 (2002) 1079–1090 On the foundations of analytical dynamics F.E. Udwadiaa; ∗, R.E. Kalabab aAerospace and Mechanical Engineering, Civil Engineering, Mathematics, and Information and Operations Management, 430K Olin Hall, University of Southern California, Los Angeles, CA 90089-1453, USA bBiomedical Engineering and Economics, University of Southern California, Los Angeles, CA 90089, USA Abstract In this paper, we present the general structure for the explicit equations of motion for general mechanical systems subjected to holonomic and non-holonomic equality constraints. The constraints considered here need not satisfy D’Alembert’s principle, and our derivation is not based on the principle of virtual work. Therefore, the equations obtained here have general applicability. They show that in the presence of such constraints, the constraint force acting on the systemcan always be viewed as madeup of the sumof two components.The explicit formfor each of the two components is provided. The ÿrst of these components is the constraint force that would have existed, were all the constraints ideal; the second is caused by the non-ideal nature of the constraints, and though it needs speciÿcation by the mechanician and depends on the particular situation at hand, this component nonetheless has a speciÿc form. The paper also provides a generalized formof D’Alembert’sprinciple which is then used to obtain the explicit equations of motion for constrained mechanical systems where the constraints may be non-ideal. We show an example where the new general, explicit equations of motion obtained in this paper are used to directly write the equations of motion for describing a non-holonomically constrained system with non-ideal constraints.
    [Show full text]
  • Recent Advances in Multi-Body Dynamics and Nonlinear Control
    Recent Advances in Multi-body Dynamics and Nonlinear Control Recent Advances in Multi-body Firdaus E. Udwadia Dynamics and Nonlinear Control Aerospace and Mechanical Engineering This paper presents some recent advances in the dynamics and control of constrained Civil Engineering,, Mathematics multi-body systems. The constraints considered need not satisfy D’Alembert’s principle Systems Architecture Engineering and therefore the results are of general applicability. They show that in the presence of and Information and Operations Management constraints, the constraint force acting on the multi-body system can always be viewed as University of Southern California, Los Angeles made up of the sum of two components whose explicit form is provided. The first of these CA 90089-1453 components consists of the constraint force that would have existed were all the [email protected] constraints ideal; the second is caused by the non-ideal nature of the constraints, and though it needs specification by the mechanician who is modeling the specific system at hand, it nonetheless has a specific form. The general equations of motion obtained herein provide new insights into the simplicity with which Nature seems to operate. They are shown to provide new and exact methods for the tracking control of highly nonlinear mechanical and structural systems without recourse to the usual and approximate methods of linearization that are commonly in use. Keywords : Constrained motion, multi-body dynamics, explicit equations of motion, exact tracking control of nonlinear systems In this paper we extend these results along two directions. First, Introduction we extend D’Alembert’s Principle to include constraints that may be, in general, non-ideal so that the forces of constraint may The general problem of obtaining the equations of motion of a therefore do positive, negative, or zero work under virtual constrained discrete mechanical system is one of the central issues displacements at any given instant of time during the motion of the in multi-body dynamics.
    [Show full text]
  • Explicit Equations of Motion for Constrained
    Explicit equations of motion for constrained mechanical systems with singular mass matrices and applications to multi-body dynamics Firdaus Udwadia, Phailaung Phohomsiri To cite this version: Firdaus Udwadia, Phailaung Phohomsiri. Explicit equations of motion for constrained mechanical systems with singular mass matrices and applications to multi-body dynamics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2006, 462 (2071), pp.2097 - 2117. 10.1098/rspa.2006.1662. hal-01395968 HAL Id: hal-01395968 https://hal.archives-ouvertes.fr/hal-01395968 Submitted on 13 Nov 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution| 4.0 International License Explicit equations of motion for constrained mechanical systems with singular mass matrices and applications to multi-body dynamics 1 2 FIRDAUS E. UDWADIA AND PHAILAUNG PHOHOMSIRI 1Civil Engineering, Aerospace and Mechanical Engineering, Mathematics, and Information and Operations Management, and 2Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA We present the new, general, explicit form of the equations of motion for constrained mechanical systems applicable to systems with singular mass matrices. The systems may have holonomic and/or non holonomic constraints, which may or may not satisfy D’Alembert’s principle at each instant of time.
    [Show full text]
  • Catalogue 176
    C A T A L O G U E – 1 7 6 JEFF WEBER RARE BOOKS Catalogue 176 Revolutions in Science THE CURRENT catalogue continues the alphabet started with cat. #174. Lots of new books are being offered here, including books on astronomy, mathematics, and related fields. While there are many inexpensive books offered there are also a few special pieces, highlighted with the extraordinary LUBIENIECKI, this copy being entirely handcolored in a contemporary hand. Among the books are the mathematic libraries of Dr. Harold Levine of Stanford University and Father Barnabas Hughes of the Franciscan order in California. Additional material is offered from the libraries of David Lindberg and L. Pearce Williams. Normally I highlight the books being offered, but today’s bookselling world is changing rapidly. Many books are only sold on-line and thus many retailers have become abscent from city streets. If they stay in the trade, they deal on-line. I have come from a tradition of old style bookselling and hope to continue binging fine books available at reasonable prices as I have in the past. I have been blessed with being able to represent many collections over the years. No one could predict where we are all now today. What is your view of today’s book world? How can I serve you better? Let me know. www.WeberRareBooks.com On the site are more than 10,000 antiquarian books in the fields of science, medicine, Americana, classics, books on books and fore-edge paintings. The books in current catalogues are not listed on-line until mail-order clients have priority.
    [Show full text]
  • Encke's Minima and Encke's Division in Saturn's A-Ring
    ENCKE’S MINIMA AND ENCKE’S DIVISION IN SATURN’S A-RING Pedro Ré http://astrosurf.com/re When viewed with the aid of a good quality telescope Saturn is undoubtedly one of the most spectacular objects in the sky. Many amateur astronomers (including the author) say that their first observation of Saturn turned them on to astronomy. Saturn’s rings are easily visible with a good 60 mm refractor at 50x. The 3D appearance of this planet is what makes it so interesting. Details in the rings can be seen during moments of good seeing. The Cassini division (between ring A and B) is easily visible with moderate apertures. The Encke minima and Encke division are more difficult to observe and require large apertures and telescopes of excellent optical quality. These two features can be observed in Saturn’s A-Ring. The Encke minima consists of a broad, low contrast feature located about halfway out in the middle of the A-Ring. The Encke division is a narrow, high contrast feature located near the outer edge of the A-Ring. Unlike the Encke minima, the Encke division is an actual division of the ring (Figure 1). Figure 1- Saturn near Opposition on June 11, 2017. D. Peach, E. Kraaikamp, F. Colas, M. Delcroix, R. Hueso, G. Thérin, C. Sprianu, S2P, IMCCE, OMP. The Encke division is visible around the entire outer A ring. Astronomy Picture of the Day (20170617) https://apod.nasa.gov/apod/ap170617.html 1 Galileo Galilei observed the disk Saturn for the first time using one of his largest refractor.
    [Show full text]