Related papers: Teaching Rotational Physics with Bivectors
Geometric torsions are torsions of acyclic complexes of vector spaces which consist of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a…
Tensor 50-component form of the first order relativistic wave equation for a particle with spin 2 and anomalous magnetic moment is extended to the case of an arbitrary curved space-time geometry. An additional parameter considered in the…
Since Galileo's time, the pendulum has evolved into one of the most exciting physical objects in mathematical modeling due to its vast range of applications for studying various oscillatory dynamics, including bifurcations and chaos, under…
Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this…
Quantum physics is considered as one of the most remarkable discoveries of contemporary physics grown during previous century and gradually manifested to the scientific world such as inventions of laser, the transistor, the electron…
A general method for the reduction of coupled spherical harmonic products is presented. When the total angular coupling is zero, the reduction leads to an explicitly real expression in the scalar products within the unit vector arguments of…
We present generalized expressions to calculate the orbital angular momentum for invariant beams using scalars potentials. The solutions can be separated into transversal electric TE, transversal magnetic TM and transversal electromagnetic…
While studying the motion of a heavy symmetric top, in general, constants of motion are used. Some students may want to understand the motion in terms of torque, which can lie on their routine based on the usage of Newton's second law.…
In teleparallelism one is able to tackle the gravitational energy and angular momentum problems in a way that distinguishes this theory from other theories of gravity, such as general relativity. However, unlike the $4$-momentum, the…
The mathematical representation of the physical objects determines which mathematical branch will be applied during the physical analysis in the systems studied. The difference among non-quantum physics, like classic or relativistic…
The classical and continuum limit of a quantum gravitational setting could lead, at mesoscopic regimes, to a very different notion of geometry w.r.t. the pseudo-Riemannian one of special and general relativity. A possible way to…
We investigate the carter like constant for a particle in a non relativistic dipolar field. This special case is a missing link between carter constant in stationary axially symmetric spacetime such as Kerr solution and its possible…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
Recently, there has been an increasing interest in employing rotational motion measurements for seismic source inversion, structural imaging and ambient noise analysis. We derive reciprocity and representation theorems for rotational…
The milq approach to quantum physics for high schools focuses on the conceptual questions of quantum physics. Students should be given the opportunity to engage with the world view of modern physics. The aim is to achieve a conceptually…
We propose a graded classification of the entire field of multivector physics, including all alternative points of view. The (often tacit) postulates of different types of formulations are contrasted, summarizing their consequences.…
The metrics of general relativity generally fall into two categories: Those which are solutions of the Einstein equations for a given source energy-momentum tensor, and the "reverse engineered" metrics -- metrics bespoke for a certain…
Light carrying orbital angular momentum (OAM)--known as vortex beams--has broadened the scope of understanding and applications of light's angular momentum. Optical tweezers using OAM, often referred to as optical spanners, have…
A theory of gravity with torsion is examined in which the torsion tensor is constructed from the exterior derivative of an antisymmetric rank two potential plus the dual of the gradient of a scalar field. Field equations for the theory are…
Simple physical models of a measuring rod and of a clock are used to demonstrate the contraction of objects and clock retardation in special relativity. It is argued that the models could help in promoting student understanding of special…