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Hamiltonian

Hamiltonian

1 9.3
Relating to William Rowan Hamilton's work in mathematics and physics
  • adjective
  • /ˌhæmɪlˈtoʊniən/
  • Specialized
: hamiltoniano
  • We now illustrate how ASP works by analyzing the problem of finding a Hamiltonian cycle in a directed graph.
  • Hamiltonian cycle
  • Hamiltonian systems

It's a deeply abstract thing and the Hamiltonian formulation of mechanics, whereas in quantum mechanics it really is very intuitive.

Examples

  • Clearly, the selected edges form a Hamiltonian cycle if and only if every pair of vertices is in the transitive closure.

    Academic text (2011)

  • Find me another Hamiltonian circuit in this graph.

  • A key part is the definition of a Hamiltonian cycle.

    Academic text (2011)

  • But what I want to work into now is the Hamiltonian form of mechanics.

  • In the Hamiltonian cycle example, we have a single, fixed program that works uniformly with all input graphs.

    Academic text (2011)

  • Chapter 1, for example, starts by discussing basic notions of Hamiltonian and Lagrangian mechanics.

    Academic text (2003)

  • It's a deeply abstract thing and the Hamiltonian formulation of mechanics, whereas in quantum mechanics it really is very intuitive.

    Stanford

  • In physics, the Hamiltonian describes the total energy of a system and is crucial for understanding its dynamics.

  • A Hamiltonian graph ensures that there is a cycle that visits each vertex exactly once.

  • The principles of Hamiltonian mechanics provide a powerful framework for solving complex physical problems.

Surface Forms

Hamiltonian positive

Morphology

Hamiltonian = Hamilton (semi-transparent) = Hamilton + ian

Morphologically straightforward (Hamilton + -ian), but the specialized academic meaning relating to a mathematician's theories requires domain knowledge beyond simple word-formation.

Etymology

Hamiltonian comes from the name Hamilton, from Sir William Rowan Hamilton, plus the ending -ian, which means 'related to'. Just like Newtonian comes from Newton, a Hamiltonian idea in math or physics is named after Hamilton and follows his work.