Related papers: Non inertial dynamics and holonomy on the ellipsoi…
We discuss a classical anisotropic oscillator and the Foucault pendulum as examples illustrating non-conservation of action variables in integrable classical mechanical systems with adiabatically slow evolution. We also emphasize the…
The somewhat fragmented body of current literature analyzing the properties of test particle motion in static and stationary spacetimes and in general spacetimes is pulled together and clarified using the framework of…
We give a simple and self contained introduction to quaternions and their practical usage in dynamics. The rigid body dynamics are presented in full details. In the appendix, some more exotic relations are given that allow to write more…
The dynamics of general Lovelock gravity, viewed on an arbitrary spherically symmetric surface as a holographic screen, is recast as the form of some generalized first law of thermodynamics on the screen. From this observation together with…
We offer some, hopefully clarifying, comments on Verlinde's recent claim that gravity is an entropic force. A suitable identification of quantities shows that both formulations of Newtonian gravity, the classical and the thermodynamical…
An alternative, scalar theory of gravitation has been proposed, based on a mechanism/interpretation of gravity as being a pressure force: Archimedes' thrust. In it, the gravitational field affects the physical standards of space and time,…
We stress that halo dipole components are nontrivial in core-halo systems in both Newton's gravity and General Relativity. To this end, we extend a recent exact relativistic model to include also a halo dipole component. Next, we consider…
Using elementary geometric tools, we apply essentially the same methods to derive expressions for the rotation angle of the swing plane of Foucault's pendulum and the rotation angle of the spin of a relativistic particle moving in a…
We consider the possibility of using Dirac's ideas of the deformation of Poisson brackets in nonholonomic mechanics. As an example, we analyze the composition of external forces that do no work and reaction forces of nonintegrable…
I describe several conceptual aspects of a particular paradigm which treats the field equations of gravity as emergent. These aspects are related to the features of classical gravitational theories which defy explanation within the…
In this paper, we address a theoretical investigation of the gravitational lensing phenomenon within the space-time framework of a holonomy-corrected spherically symmetric black hole (BH), incorporating both ordinary and phantom global…
The two equations of motion for a test particle are compared with each other. One is in the Non commutative space involving a static rigid sphere (as a source of central force) and the other is in the usual space involving a slowly…
The nonlocal electrodynamics of uniformly rotating systems is presented and its predictions are discussed. In this case, due to paucity of experimental data, the nonlocal theory cannot be directly confronted with observation at present. The…
Fractional dynamics of relativistic particle is discussed. Derivatives of fractional orders with respect to proper time describe long-term memory effects that correspond to intrinsic dissipative processes. Relativistic particle subjected to…
The geodesic equations are integrated for the Lewis metric and the effects of the different parameters appearing in the Weyl class on the motion of test particles are brought out. Particular attention deserves the appearance of a force…
We study the introduction of holonomy corrections in $f(R)$ gravity. We will show that there are infinitely many ways, as many as canonical transformations, to introduce this kind of corrections, depending on the canonical variables (two…
We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…
We review the recent developments in applying holographic methods to understand non-equilibrium physics in strongly coupled field theories. The emphasis will be on elucidating the relation between evolution of quantum field theories…
We consider a maximal extension of the Hilbert-Einstein action and analyze several interesting features of the theory. More specifically, the motion is non-geodesic and takes place in the presence of an extra force. These models could lead…
Non-Hermitian Hamiltonians provide an alternative perspective on the dynamics of quantum and classical systems coupled non-conservatively to an environment. Once primarily an interest of mathematical physicists, the theory of non-Hermitian…