R H HAMILTON
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Sir William Rowan Hamilton (4 August 1805 – 2 September 1865) was an Irish astronomer, mathematician, and physicist who made numerous major contributions to abstract algebra, classical mechanics, and optics. His theoretical works and mathematical equations are considered fundamental to modern theoretical physics, particularly his reformulation of Lagrangian mechanics. His career included the analysis of geometrical optics, Fourier analysis, and quaternions, the last of which made him one of the founders of modern linear algebra. Hamilton was Andrews Professor of Astronomy at Trinity College Dublin. He was also the third director of Dunsink Observatory from 1827 to 1865. The Hamilton Institute at Maynooth University is named after him.
In connection with: William Rowan Hamilton
Title combos: William Rowan Hamilton Rowan William
Description combos: works classical an 1805 director fundamental and his and
In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard bold by H . {\displaystyle \mathbb {H} .} Quaternions are not a field, because multiplication of quaternions is not, in general, commutative. Quaternions provide a definition of the quotient of two vectors in a three-dimensional space. Quaternions are generally represented in the form a + b i + c j + d k , {\displaystyle a+b\,\mathbf {i} +c\,\mathbf {j} +d\,\mathbf {k} ,} where the coefficients a, b, c, d are real numbers, and 1, i, j, k are the basis vectors or basis elements. Quaternions are used in pure mathematics, but also have practical uses in applied mathematics, particularly for calculations involving three-dimensional rotations, such as in three-dimensional computer graphics, computer vision, robotics, magnetic resonance imaging and crystallographic texture analysis. They can be used alongside other methods of rotation, such as Euler angles and rotation matrices, or as an alternative to them, depending on the application. In modern terms, quaternions form a four-dimensional associative normed division algebra over the real numbers, and therefore a ring, also a division ring and a domain. It is a special case of a Clifford algebra, classified as Cl 0 , 2 ( R ) ≅ Cl 3 , 0 + ( R ) . {\displaystyle \operatorname {Cl} _{0,2}(\mathbb {R} )\cong \operatorname {Cl} _{3,0}^{+}(\mathbb {R} ).} It was the first noncommutative division algebra to be discovered. According to the Frobenius theorem, the algebra H {\displaystyle \mathbb {H} } is one of only two finite-dimensional division rings containing a proper subring isomorphic to the real numbers; the other being the complex numbers. These rings are also Euclidean Hurwitz algebras, of which the quaternions are the largest associative algebra (and hence the largest ring). Further extending the quaternions yields the non-associative octonions, which is the last normed division algebra over the real numbers. The next extension gives the sedenions, which have zero divisors and so cannot be a normed division algebra. The unit quaternions give a group structure on the 3-sphere S3 isomorphic to the groups Spin(3) and SU(2), i.e. the universal cover group of SO(3). The positive and negative basis vectors form the eight-element quaternion group.
In connection with: Quaternion
Description combos: and to vectors system multiplication form It S3 divisors
In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion, Lagrangian mechanics and Hamiltonian mechanics. The Hamilton–Jacobi equation is a formulation of mechanics in which the motion of a particle can be represented as a wave. In this sense, it fulfilled a long-held goal of theoretical physics (dating at least to Johann Bernoulli in the eighteenth century) of finding an analogy between the propagation of light and the motion of a particle. The wave equation followed by mechanical systems is similar to, but not identical with, the Schrödinger equation, as described below; for this reason, the Hamilton–Jacobi equation is considered the "closest approach" of classical mechanics to quantum mechanics. The qualitative form of this connection is called Hamilton's optico-mechanical analogy. In mathematics, the Hamilton–Jacobi equation is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations. It can be understood as a special case of the Hamilton–Jacobi–Bellman equation from dynamic programming.
In connection with: Hamilton–Jacobi equation
Title combos: equation Jacobi Hamilton Jacobi equation
Description combos: mechanics it equation of analogy In formulation physics the
Sir Hamilton Alexander Rosskeen Gibb (2 January 1895 – 22 October 1971), known as H. A. R. Gibb, was a Scottish historian and Orientalist.
In connection with: H. A. R. Gibb
Description combos: was Scottish was 1971 and Sir Hamilton as and
The name Hamilton probably originated in the village of Hamilton, Leicestershire, England, but bearers of that name became established in the 13th century in Lanarkshire, Scotland. The town of Hamilton, South Lanarkshire was named after the family some time before 1445. Contemporary Hamiltons are either descended from the original noble family, or descended from people named after the town.
In connection with: Hamilton (name)
Title combos: Hamilton name
Description combos: probably in originated village the bearers or town town
Robert Houston Hamilton (December 25, 1873 – June 15, 1946) was an American college football coach, law professor, and judge. He was the first head football coach at Baylor University, serving from 1899 to 1900 and compiling a record of 5–1–1. Hamilton graduated from Baylor's law department in 1899 and joined the faculty of Baylor Law School in 1900. After leaving Baylor, he moved to Port Lavaca, Texas, where he served as a county judge before attending the University of Chicago. In 1921, he was elected to the Texas Supreme Court. Hamilton died on June 15, 1946, at his home in Port Lavaca.
In connection with: R. H. Hamilton
Description combos: from 25 where 1946 in served the and 1900
Hamilton Morris (born April 14, 1987) is an American journalist, documentarian, and scientific researcher. He is the creator and director of the television series Hamilton's Pharmacopeia, in which he investigated the chemistry, history, and cultural impact of various psychoactive drugs. Morris is considered to be one of the world's leading drug journalists.
In connection with: Hamilton Morris
Title combos: Hamilton Morris
Description combos: leading psychoactive various Hamilton which journalist investigated an April
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