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9772 results in Engineering: general interest

Page 139 of 489

  • 4 - Covariant and contravariant vector components

  • Daniel A. Fleisch, Wittenberg University, Ohio
  • Book:
    A Student's Guide to Vectors and Tensors
    Published online:
    05 June 2012
    Print publication:
    22 September 2011, pp 97-131

  • Summary

    The vector concepts and techniques described in the previous chapters are important for two reasons: they allow you to solve a wide range of problems in physics and engineering, and they provide a foundation on which you can build an understanding of tensors (the “facts of the universe”). To achieve that understanding, you'll have to move beyond the simple definition of vectors as objects with magnitude and direction. Instead, you'll have to think of vectors as objects with components that transform between coordinate systems in specific and predictable ways. It's also important for you to realize that vectors can have more than one kind of component, and that those different types of component are defined by their behavior under coordinate transformations.

    So this chapter is largely about the different types of vector component, and those components will be a lot easier to understand if you have a solid foundation in the mathematics of coordinate-system transformation.

    Coordinate-system transformations

    In taking the step from vectors to tensors, a good place to begin is to consider this question: “What happens to a vector when you change the coordinate system in which you're representing that vector?” The short answer is that nothing at all happens to the vector itself, but the vector's components may be different in the new coordinate system. The purpose of this section is to help you understand how those components change.

  • 3 - Vector applications

  • Daniel A. Fleisch, Wittenberg University, Ohio
  • Book:
    A Student's Guide to Vectors and Tensors
    Published online:
    05 June 2012
    Print publication:
    22 September 2011, pp 62-96

  • Summary

    The real value of understanding vectors and how to manipulate them becomes clear when you realize that your knowledge allows you to solve a variety of problems that would be much more difficult without vectors. In this chapter, you'll find detailed explanations of four such problems: a mass sliding down an inclined plane, an object moving along a curved path, a charged particle in an electric field, and a charged particle in a magnetic field. To solve these problems, you'll need many of the vector concepts and operations described in Chapters 1 and 2.

    Mass on an inclined plane

    Consider the delivery woman pushing a heavy box up the ramp to her delivery truck, as illustrated in Figure 3.1. In this situation, there are a number of forces acting on the box, so if you want to determine how the box will move, you need to know how to work with vectors. Specifically, to solve problems such as this, you can use vector addition to find the total force acting on the box, and then you can use Newton's Second Law to relate that total force to the acceleration of the box.

    To understand how this works, imagine that the delivery woman slips off the side of the ramp, leaving the box free to slide down the ramp under the influence of gravity.

Memoirs of Richard Lovell Edgeworth, Esq
  • Begun by Himself and Concluded by his Daughter, Maria Edgeworth
  • Volume 2
  • Richard Lovell Edgeworth, Maria Edgeworth
  • Published online:
    07 September 2011
    Print publication:
    24 February 2011
    First published in:
    1820
  • Richard Lovell Edgeworth (1744–1817) was a noted Irish educationalist, engineer and inventor. This two-volume autobiography, begun in 1808, was published in 1820. Edgeworth had abandoned the project in 1809, having covered the period to 1781, and it was completed after his death by his eldest daughter, a successful novelist. Maria Edgeworth and her father had co-authored educational works, and the experience of helping her father run their estate during her teens had provided material for her novels. Volume 2 of these memoirs was wholly written by her, though it contains excerpts from Richard's correspondence. It recounts how, after his third marriage, the growing family returned to Ireland, and focused first on domestic and educational concerns. Richard became involved in Irish politics and the newly founded Royal Irish Academy but continued to publish essays on scientific and mechanical topics, as well as influential (though controversial) works on education.

Recollections of Forty Years
  • Volume 1
  • Ferdinand de Lesseps
  • Translated by C. B. Pitman
  • Published online:
    07 September 2011
    Print publication:
    10 March 2011
    First published in:
    1887
  • The French diplomat and engineer Ferdinand de Lesseps (1805–1894) was instrumental in the successful completion of the Suez Canal, which reduced by 3000 miles the distance by sea between Bombay and London. This two-volume memoir, written towards the end of his life and dedicated to his children, was published in this English translation in 1887. In it, de Lesseps describes his experiences in Europe and North Africa. He includes reflections on European and colonial history and politics, a chapter on steam power, and a report on the 1879 Paris conference that led to a controversial and abortive early attempt to build the Panama Canal. Volume 1 focuses on de Lesseps' diplomatic missions to Rome and Madrid in the late 1840s during a period of political and social unrest in Italy, Spain and France, and the early stages of the Suez canal project.

Narrative of an Excursion to the Lake Amsanctus and to Mount Vultur in Apulia in 1834
  • Charles Daubeny
  • Published online:
    07 September 2011
    Print publication:
    30 June 2011
    First published in:
    1835
  • This short but distinctive paper was published in 1835 by Charles Daubeny (1795–1867), who began his career as a physician but soon found his passion to be volcanos. At this time, Daubeny held chairs in chemistry and botany at Oxford. He had made many field trips to European volcanic regions between 1819 and 1825, was elected a Fellow of the Royal Society in 1822, and in 1826 published the first edition of his famous Description of Active and Extinct Volcanos, of which a later version also appears in this series. Here Daubeny describes a winter trip to the Apulia (Puglia) region in the south-east of Italy, rarely described by travel writers of his time, to visit Lake Amsanctus, famously mentioned by Virgil, and the extinct volcano Mount Vultur. Although Daubeny's overall focus is scientific, his account also includes lively descriptions of classical remains and rural society in southern Italy.

Electromagnetic Theory
  • Volume 2
  • Oliver Heaviside
  • Published online:
    07 September 2011
    Print publication:
    02 June 2011
    First published in:
    1899
  • Oliver Heaviside FRS (1850–1925) was a scientific maverick and a gifted self-taught electrical engineer, physicist and mathematician. He patented the co-axial cable, pioneered the use of complex numbers for circuit analysis, and reworked Maxwell's field equations into the more concise format we use today. In 1891 the Royal Society made him a Fellow for his mathematical descriptions of electromagnetic phenomena. Along with Arthur Kennelly, he also predicted the existence of the ionosphere. Often dismissed by his contemporaries, his work achieved wider recognition when he received the inaugural Faraday Medal in 1922. Published in 1899, the second of three volumes of Heaviside's collected work argues that physical problems (such as the age of the Earth) drive mathematical ideas, and then goes on to compare the propagation of electromagnetic waves with physical analogues.

The Works of John Playfair
  • Volume 2
  • John Playfair
  • Edited by James G. Playfair
  • Published online:
    07 September 2011
    Print publication:
    30 June 2011
    First published in:
    1822
  • John Playfair (1748–1819) was a Scottish mathematician and geologist best known for his defence of James Hutton's geological theories. He attended the University of St Andrews, completing his theological studies in 1770. In 1785 he was appointed joint Professor of Mathematics at the University of Edinburgh, and in 1805 he was elected Professor of Natural Philosophy. A Fellow of the Royal Society, he was acquainted with continental scientific developments, and was a prolific writer of scientific articles in the Transactions of the Royal Society of Edinburgh and the Edinburgh Review. This four-volume edition of his works was published in 1822 and is prefaced by a biography of Playfair. Volume 2 contains the incomplete Dissertation exhibiting a general view of the progress of mathematical and physical science, which was included as a supplement to the Encyclopaedia Britannica.

The Chemistry of Light and Photography in their Application to Art, Science, and Industry
  • Hermann Vogel
  • Published online:
    07 September 2011
    Print publication:
    19 May 2011
    First published in:
    1883
  • First published in 1875, this book describes the history and science of photography, with an emphasis on the practical processes involved and their relation to the physical and chemical properties of light. Hermann Vogel (1834–1898), who pioneered the technology for colour photography, was Professor of Photography at the Royal Industrial Academy of Berlin. Here he explains the science of photography simply and concisely for a popular readership. The book has 100 illustrations, including both woodcuts and 'specimens of the latest discoveries in photography', intended to demonstrate the value of the technology to society. It traces the history of photography from its beginnings in experiments conducted by Davy and Wedgwood and the invention of the Daguerreotype to the most recent developments of Vogel's day. It was regarded as the most comprehensive guide to photography then available, and ran to several editions. This reissue is of the fourth edition of 1883.

The Works of John Playfair
  • Volume 4
  • John Playfair
  • Edited by James G. Playfair
  • Published online:
    07 September 2011
    Print publication:
    30 June 2011
    First published in:
    1822
  • John Playfair (1748–1819) was a Scottish mathematician and geologist best known for his defence of James Hutton's geological theories. He attended the University of St Andrews, completing his theological studies in 1770. In 1785 he was appointed joint Professor of Mathematics at the University of Edinburgh, and in 1805 he was elected Professor of Natural Philosophy. A Fellow of the Royal Society, he was acquainted with continental scientific developments, and was a prolific writer of scientific articles in the Transactions of the Royal Society of Edinburgh and the Edinburgh Review. This four-volume edition of his works was published in 1822 and is prefaced by a biography of Playfair. Volume 4 contains his biographies of his colleagues, and review articles on mathematical and astronomical works, both in English and French.

Electromagnetic Theory
  • Volume 1
  • Oliver Heaviside
  • Published online:
    07 September 2011
    Print publication:
    02 June 2011
    First published in:
    1893
  • Oliver Heaviside FRS (1850–1925) was a scientific maverick and a gifted self-taught electrical engineer, physicist and mathematician. He patented the co-axial cable, pioneered the use of complex numbers for circuit analysis, and reworked Maxwell's field equations into a more concise format. In 1891 the Royal Society made him a Fellow for his mathematical descriptions of electromagnetic phenomena. Along with Arthur Kennelly, he also predicted the existence of the ionosphere. Often dismissed by his contemporaries, his work achieved wider recognition when he received the inaugural Faraday Medal in 1922. Published 1893 this is the first of three volumes that bring together Heaviside's contributions to electromagnetic theory. It introduces the subject at length, and features his first description of vector analysis and the reworking of Maxwell's field equations into the form we know today.

The Life of Sir Humphry Davy
  • Volume 2
  • John Ayrton Paris
  • Published online:
    07 September 2011
    Print publication:
    02 June 2011
    First published in:
    1831
  • Sir Humphry Davy (1778–1829) was a hugely influential chemist, inventor, and public lecturer who is recognised as one of the first professional scientists. He was apprenticed to an apothecary in 1795, which formed his introduction to chemical experiments. A chance meeting with Davis Giddy in 1798 introduced Davy into the wider scientific community, and in 1800 he was invited to a post at the Royal Institution, where he lectured to great acclaim. These volumes, first published in 1831, contain Davy's official biography. Researched and written by John Ayrton Paris, the work describes in detail Davy's life and his scientific studies. Organised chronologically with excerpts from his private correspondence, Davy's early life and his experiments and lectures at the Royal Institution and his Presidency of the Royal Society between 1820 and 1827 are explored in vivid detail. Volume 2 describes his life and work between 1812 and 1829.

The Life of Sir Humphry Davy
  • Volume 1
  • John Ayrton Paris
  • Published online:
    07 September 2011
    Print publication:
    02 June 2011
    First published in:
    1831
  • Sir Humphry Davy (1778–1829) was a hugely influential chemist, inventor, and public lecturer who is recognised as one of the first professional scientists. He was apprenticed to an apothecary in 1795, which formed his introduction to chemical experiments. A chance meeting with Davis Giddy in 1798 introduced Davy into the wider scientific community, and in 1800 he was invited to a post at the Royal Institution, where he lectured to great acclaim. These volumes, first published in 1831, contain Davy's official biography. Researched and written by John Ayrton Paris, the work describes in detail Davy's life and his scientific studies. Organised chronologically with excerpts from his private correspondence, Davy's early life and his experiments and lectures at the Royal Institution and his Presidency of the Royal Society between 1820 and 1827 are explored in vivid detail. Volume 1 describes his life and work until 1812.

Correspondence of Josiah Wedgwood
  • Volume 1, Letters of Josiah Wedgwood 1762 to 1772
  • Josiah Wedgwood
  • Edited by Katherine Eufemia Farrer
  • Published online:
    07 September 2011
    Print publication:
    20 January 2011
    First published in:
    1903
  • Josiah Wedgwood (1730–1795) was a master potter who pioneered the industrialisation of pottery manufacture during the early Industrial Revolution. His experimental work on ceramics resulted in many innovations in the production and decoration of pottery. This three-volume work, edited by his great-granddaughter Katherine Eufemia Farrer and first published between 1903 and 1906, contains Wedgwood's letters to his business partner, the Liverpool merchant Thomas Bentley (1730–1780). Wedgwood's highly successful partnership with Bentley is credited with the expansion and development of Wedgwood's reputation across Europe. The letters cover the years 1762 to 1794 and provide a lively account both of the growth of the business partnership and of Wedgwood's domestic life. Wedgwood and Bentley also maintained a keen interest in current affairs, and these volumes provide a fascinating glimpse into the society and domestic life of the late eighteenth century. Volume 1 covers 1762–1772.

Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton
  • Volume 1
  • David Brewster
  • Published online:
    07 September 2011
    Print publication:
    16 December 2010
    First published in:
    1855
  • Sir David Brewster (1781–1868) was a Scottish physicist, mathematician, astronomer, inventor, and writer of international reputation. His biography of Sir Isaac Newton, published in 1855 and reissued in 1860, was the result of over twenty years' research, undertaken while publishing hundreds of scientific papers of his own. Brewster made use of previously unknown correspondence by Newton, and his own scientific interests, particularly in optics, meant that he was able to understand and explain Newton's work. It covered the many facets of Newton's personality and work, remaining the best available study of Newton for over a century. Brewster reveals much about the science of his own time in his handling of earlier centuries, and as a cleric was obviously uncomfortable about the evidence of Newton's unorthodox religious views and alchemical studies. Volume 1 covers the period up to about 1700, and includes disputes with Leibniz over the development of calculus.

Recollections of Forty Years
  • Volume 2
  • Ferdinand de Lesseps
  • Translated by C. B. Pitman
  • Published online:
    07 September 2011
    Print publication:
    10 March 2011
    First published in:
    1887
  • The French diplomat and engineer Ferdinand de Lesseps (1805–1894) was instrumental in the successful completion of the Suez Canal, which reduced by 3000 miles the distance by sea between Bombay and London. This two-volume memoir, written towards the end of his life and dedicated to his children, was published in this English translation in 1887. In it, de Lesseps describes his experiences in Europe and North Africa. He includes reflections on European and colonial history and politics, an essay on steam power, and a report on the 1879 Paris conference that led to a controversial and abortive early attempt by a French company to build the Panama Canal. Volume 2 focuses on the Suez project, quoting extensively from de Lesseps' correspondence, and also contains facts and figures relating to the 'interoceanic canal', political essays, and the speeches for his inauguration into the Académie française.

The Suez Canal
  • Letters and Documents Descriptive of its Rise and Progress in 1854–1856
  • Ferdinand de Lesseps
  • Translated by N. D’Anvers
  • Published online:
    07 September 2011
    Print publication:
    24 February 2011
    First published in:
    1876
  • In the early 1850s the French diplomat and engineer Ferdinand de Lesseps (1805–1894) revived earlier French plans to build a canal through the Isthmus of Suez. He saw the immense benefits such a canal would bring, reducing by 3000 miles the distance by sea between Bombay and London, and he was instrumental in its successful completion. These letters, published in this English translation in 1876, show how De Lesseps persuaded the Viceroy of Egypt to allow construction, and how he overcame opposition from Britain and Turkey. Letters to the Viceroy, Emperor Napoleon III, Members of Parliament, diplomats, and politicians throughout Europe, together with more personal letters to his wife, all illustrate his resolute determination to see his project succeed. This is an invaluable source, not only on the canal, but also on the politics of the major powers and European attitudes towards the Middle East and its people.

The Architectural History of Canterbury Cathedral
  • Robert Willis
  • Published online:
    07 September 2011
    Print publication:
    02 December 2010
    First published in:
    1845
  • Canterbury Cathedral, at the heart of the Church in England since the arrival of Augustine in Kent in 597 C.E., is remarkable for its extent, beauty and importance, for the variety of its architectural styles and the many structural changes which it has undergone over the years. In this 1845 work, the Reverend Robert Willis, who was Jacksonian Professor of the University of Cambridge, reproduces historical accounts of the destruction and rebuilding of the cathedral, for example by the monk and chronicler Gervase of Canterbury on the disastrous fire in 1174. He connects these sources to his own informed opinions and interpretations of the historical documents, and includes many illustrative wood engravings to aid the discussion. The modern reader will obtain a great insight into the motives that dictated such changes of plan and structure of this incredible building.

Page 139 of 489