Related papers: Hill's equation, tire tracks and rolling cones
The properties of the equation of Dirac type in three-dimensional and five-dimensional Minkowski space-time with respect to time reflection (in sense of Pauli and Wigner) as well as to the operation of charge conjugation are investigated.…
Motion of curves and surfaces in $\R^3$ lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the continuum limit and integrable soliton systems through…
Rigidity results for asymptotically locally hyperbolic manifolds with lower bounds on scalar curvature are proved using spinor methods related to the Witten proof of the positive mass theorem. The argument is based on a study of the Dirac…
Vorticity filament motions with respect to the Dirac bracket of Rasetti and Regge [1975] are known to be related to the nonlinear Schr\"odinger equation by the Hasimoto transformation (HT), when the Hamiltonian is the Local Induction…
The nonlinear Schrodinger equation is well known as a universal equation in the study of wave motion. In the context of wave motion at the free surface of an incompressible fluid, the equation accurately predicts the evolution of modulated…
Defining Lorentzian Sabban frame of the unit speed time-like curves on de Sitter 2-space $\mathbb{S}^{2}_{1}$ and introducing space-like height function on the unit speed time-like curves on $\mathbb{S}^{2}_{1}$, the invariants of the unit…
In this article we first develop novel Rindler-type representations of flat spacetime by demonstrating that the standard hyperbolic transformation is a member of an infinite family of coordinate mappings. We specifically introduce cyclic…
At first we introduce the space-time manifold and we compare some aspects of Riemannian and Lorentzian geometry such as the distance function and the relations between topology and curvature. We then define spinor structures in general…
A Hamiltonian formulation is given for the gravitational dynamics of two spinning compact bodies to next-to-leading order ($G/c^4$ and $G^2/c^4$) in the spin-orbit interaction. We use a novel approach (valid to linear order in the spins),…
We show that Poincar\'e invariance directly implies the existence of a complexified Minkowski space whose real and imaginary directions unify spacetime and spin, which we dub spinspacetime. Despite the intrinsic noncommutativity of spin,…
The basic notion for a motion of a heavy rigid body fixed at a point in three-dimensional space as well as its higher-dimensional generalizations are presented. On a basis of Lax representation, the algebro-geometric integration procedure…
In this paper, the dynamical equations and junction conditions at the interface between adjacent layers of different elastic properties for an elastic deformable astronomical body in the first post-Newtonian approximation of Einstein theory…
We discuss constants of motion of a particle under an external field in a curved spacetime, taking into account the Hamiltonian constraint which arises from reparametrization invariance of the particle orbit. As the necessary and sufficient…
The moving lemma of Suslin states that a cycle on $X\times \mathbb{A} ^n$ meeting all faces properly can be moved so that it becomes equidimensional over $\mathbb{A}^n$. This leads to an isomorphism of motivic Borel-Moore homology and…
The motion of a rigid body in a quadratic potential is an important example of an integrable Hamiltonian system on a dual to a semidirect product Lie algebra so(n) x Symm(n). We give a Lagrangian derivation of the corresponding equations of…
A novel but elementary geometric construction produces on the seven-dimensional manifold of rotated spheres in Euclidean three-space a finslerian geometry whose geodesics are interpreted as the paths of free, spinning, spherical particles…
By means of the method of moving Frenet-Serret frame the set of equations of motion is derived for spinning particle in an arbitrary external field, which is determined by potential depending from both position and the state of movement, as…
In this work, Einstein's view of geometry as physical geometry is taken into account in the analysis of diverse issues related to the notions of inertial motion and inertial reference frame. Einstein's physical geometry enables a…
Dynamics is considered as a corollary of the space-time geometry. Evolution of a particle in the space-time is described as a chain of connected equivalent geometrical objects. Space-time geometry is determined uniquely by the world…
The spin-curvature coupling as captured by the so-called Mathisson-Papapetrou-Dixon (MPD) equations is the leading order effect of the finite size of a rapidly rotating compact astrophysical object moving in a curved background. It is also…