Classical Hamiltonian quaternions information

Hamilton invented quaternions, a mathematical entity in 1843. This article describes Hamilton's original treatment of quaternions, using his notation...

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...

and quaternions, the last of which made him one of the founders of modern linear algebra. He has made major contributions in optics, classical mechanics...

expressions are referred to classical Hamiltonian quaternions. Hamilton's innovation consisted of expressing quaternions as an algebra over R. The formulae...

\mathbb {R} } , the complex numbers C {\displaystyle \mathbb {C} } and the quaternions H {\displaystyle \mathbb {H} } together with special automorphism groups...

matrix Hamiltonian numbers (or quaternions) In physics: Hamiltonian constraint Hamiltonian fluid mechanics Hamiltonian operator, see Hamiltonian (quantum...

phase space. Hamiltonian mechanics Metaplectic group Orthogonal group Paramodular group Projective unitary group Representations of classical Lie groups...

subspace. As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford...

generated by iσ1, iσ2, iσ3 functions identically (is isomorphic) to that of quaternions ( H {\displaystyle \mathbb {H} } ). All three of the Pauli matrices can...

classical potential energy term, as well as momentum terms like the classical kinetic energy term. A key difference is that relativistic Hamiltonians...

Theorie der vielfachen Kontinuität, and Hamilton's discovery of the quaternions and John T. Graves' discovery of the octonions in 1843 marked the beginning...

to represent orientations, rotation quaternions are typically called orientation quaternions or attitude quaternions. To consider rigid body dynamics in...

Jordan–Hölder theorem. Dedekind and Miller independently characterized Hamiltonian groups and introduced the notion of the commutator of two elements. Burnside...

entry into mathematical physics with a vector-based introduction to quaternions and a primer on matrix notation for linear transformations of 4-vectors...

associative division algebras are the real numbers, complex numbers and quaternions.: 366  As STA is not a division algebra, some STA elements may lack an...

fields, and fluid flow. Vector calculus was developed from the theory of quaternions by J. Willard Gibbs and Oliver Heaviside near the end of the 19th century...

numbers (i.e. the complex numbers C {\displaystyle \mathbb {C} } , the quaternions H {\displaystyle \mathbb {H} } , and the octonions O {\displaystyle \mathbb...

orientation of a rigid body, including a set of three Euler angles, a quaternion, or a direction cosine matrix (also referred to as a rotation matrix)...

Newtonian mechanics, now called Hamiltonian mechanics. This work has proven central to the modern study of classical field theories such as electromagnetism...

composed of quaternions, H = (Hij)n i,j=1. Its distribution is invariant under conjugation by the symplectic group, and it models Hamiltonians with time-reversal...

{\displaystyle S^{3}} ; as a group, it may be identified with the group of unit quaternions. The Heisenberg group is a connected nilpotent Lie group of dimension...