Engineering Calculus Notes 34

Engineering Calculus Notes 34 - e.g areas of surfaces in...

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22 CHAPTER 1. COORDINATES AND VECTORS Figure 1.17: Combining Displacements Aristotle (384-322 BC ) [ 24 , vol. I, p. 344], and is discussed at some length in the Mechanics by Heron of Alexandria ( ca. 75 AD ) [ 24 , vol. II, p. 348]. The vectorial nature of some physical quantities, such as velocity, acceleration and force, was well understood and used by Isaac Newton (1642-1727) in the Principia [ 39 , Corollary 1, Book 1 (p. 417)]. In the late eighteenth and early nineteenth century, Paolo Frisi (1728-1784), Leonard Euler (1707-1783), Joseph Louis Lagrange (1736-1813), and others realized that other physical quantities, associated with rotation of a rigid body (torque, angular velocity, moment of a force), could also be usefully given vectorial representations; this was developed further by Louis Poinsot (1777-1859), Sim´ eon Denis Poisson (1781-1840), and Jacques Binet (1786-1856). At about the same time, various geometric quantities (
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Unformatted text preview: e.g. , areas of surfaces in space) were given vectorial representations by Gaetano Giorgini (1795-1874), Simon Lhuilier (1750-1840), Jean Hachette (1769-1834), Lazare Carnot (1753-1823)), Michel Chasles (1793-1880) and later by Hermann Grassmann (1809-1877) and Giuseppe Peano (1858-1932). In the early nineteenth century, vectorial representations of complex numbers (and their extension, quaternions) were formulated by several researchers; the term vector was coined by William Rowan Hamilton (1805-1865) in 1853. Finally, extensive use of vectorial properties of electromagnetic forces was made by James Clerk Maxwell (1831-1879) and Oliver Heaviside (1850-1925) in the late nineteenth century. However, a general theory of vectors was only formulated in the very late nineteenth...
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