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The study of the hodograph, as a method of investigating the motion of a body, was introduced by Sir W. R. Hamilton. The hodograph may be defined as the path traced out by the extremity of a vector which continually represents, in direction and magnitude, the velocity of a moving body.
Clayton Hamilton, in A Manual of The Art of Fiction (1918), stated that a proper plot outline is, "A plot, therefore, in its general aspects, may be figured as a complication followed by an explication, a tying followed by an untying, or (to say the same thing in French words which are perhaps more connotative) a nouement followed by a ...
Hamilton opened to positive reviews on Broadway. A review in the New York Post read, "Congratulations are due to Mary Hamlin and George Arliss upon the cordial public reception accorded to their play 'Hamilton,' upon the occasion of its first production in this city ... The piece is a welcome and, in some respects, notable addition to the small ...
A Hamiltonian system is a dynamical system governed by Hamilton's equations. In physics, this dynamical system describes the evolution of a physical system such as a planetary system or an electron in an electromagnetic field. These systems can be studied in both Hamiltonian mechanics and dynamical systems theory.
For a Hamiltonian decomposition to exist in an undirected graph, the graph must be connected and regular of even degree.A directed graph with such a decomposition must be strongly connected and all vertices must have the same in-degree and out-degree as each other, but this degree does not need to be even.
The symplectic structure induces a Poisson bracket. The Poisson bracket gives the space of functions on the manifold the structure of a Lie algebra. If F and G are smooth functions on M then the smooth function ω(J(dF), J(dG)) is properly defined; it is called a Poisson bracket of functions F and G and is denoted {F, G}. The Poisson bracket ...
Hamilton's invention of the game came from his studies of symmetry, and from his invention of the icosian calculus, a mathematical system describing the symmetries of the dodecahedron. Hamilton sold his work to a game manufacturing company, and it was marketed both in the UK and Europe, but it was too easy to become commercially successful.
A diffeomorphism between two symplectic manifolds: (,) (, ′) is called a symplectomorphism if ′ =, where is the pullback of .The symplectic diffeomorphisms from to are a (pseudo-)group, called the symplectomorphism group (see below).