Related papers: Lagrangian Mechanics on Quaternion Kaehler Manifol…
Newtonian, Lagrangian, and Hamiltonian dynamical systems are well formalized mathematically. They give rise to geometric structures describing motion of a point in smooth manifolds. Riemannian metric is a different geometric structure…
A method of reducing general quaternion functions of first degree, i.e., linear quaternion functions, to quaternary canonical form is given. Linear quaternion functions, once reduced to canonical form, can be maintained in this form under…
In this paper, we introduce the notion of quaternion shearlet transform- which is an extension of the ordinary shearlet transform. Firstly, we study the fundamental properties of quaternion shearlet transforms and then establish some basic…
We develop a theory of gauge and dynamical equivalence for Lagrangian systems on Lie algebroids, also studying its relationship with Noether and non-Noether conserved quantities.
This paper aims at the most comprehensive and systematic construction and tabulation of mechanical systems that admit a second invariant, quadratic in velocities, other than the Hamiltonian. The configuration space is in general a 2D…
The Lagrangian formulation of classical mechanics is widely applicable in solving a vast array of physics problems encountered in the undergraduate and graduate physics curriculum. Unfortunately, many treatments of the topic lack…
We show that, in quaternion quantum mechanics with a complex geometry, the minimal four Higgs of the unbroken electroweak theory naturally determine the quaternion invariance group which corresponds to the Glashow group. Consequently, we…
This paper contains results on geometric Routh reduction and it is a continuation of a previous paper where a new class of transformations is introduced between Lagrangian systems obtained after Routh reduction. In general, these reduced…
An explicit Lagrangian description is given for the Heisenberg equation on the algebra of operators of a quantum system, and for the Landau-von Neumann equation on the manifold of quantum states which are isospectral with respect to a fixed…
The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We…
This paper presents Hamilton dynamics on Clifford Kaeler manifolds. In the end, the some results related to Clifford Kaehler dynamical systems are also discussed.
We discuss the dynamics of a particular two-dimensional (2D) physical system in the four dimensional (4D) (non-)commutative phase space by exploiting the consistent Hamiltonian and Lagrangian formalisms based on the symplectic structures…
This dissertation is about The history of quaternions and their associated rotation groups as it relates to theoretical physics.
It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian…
While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and…
The purpose of the present paper is to study the differential geometric properties of a quaternion CR-submanifold in a locally conformal quaternion Kaehler manifold.
A new approach to relativistic mechanics is proposed, suitable to describe dynamics of different kinds of relativistic particles. Mathematically it is based on an application of the recent geometric theory of nonholonomic systems on fibred…
We explain the use of dual quaternions to represent poses, twists, and wrenches.
In this study, Lagrangian and Hamiltonian systems, which are mathematical models of mechanical systems, were introduced on the horizontal and the vertical distributions of tangent and cotangent bundles. Finally, some geometrical and…