Related papers: Least-action perihelion precession
The particles of a classical relativistic gas are supposed to move under the influence of a quasilinear (in the particle four-momenta), self-interacting force inbetween elastic, binary collisions. This force which is completely fixed by the…
We postulate that all the presently known kinematic effects on physical quantities related to a material particle (e.g., masss increase) are due to its velocity relative to surrounding matter, and not to the observer's reference frame. The…
The least action principle is established for the dynamics of a test particle in a dilaton-Maxwell background. These dynamics and background are invariant under the action of the dilatation transformation; explicit form of the corresponding…
We consider a coplanar system comprised of a massive central body (a star), a less massive secondary (a planet) on a circular orbit, and a test particle on a bound orbit exterior to that of the secondary. The gravitational pull exerted on…
Three radii are associated with a circle: the "geodesic radius" R_1 which is the distance from circle's center to its perimeter, the "circumferential radius" R_2 which is the length of the perimeter divided by 2 pi and the "curvature…
A body dissipates energy when it freely rotates about any axis different from principal. This entails relaxation, i.e., decrease of the rotational energy, with the angular momentum preserved. The spin about the major-inertia axis…
The evidence is that the mass of the universe is dominated by an exotic nonbaryonic form of matter largely draped around the galaxies. It approximates an initially low pressure gas of particles that interact only with gravity, but we know…
Using Peebles' least action principle, we determine trajectories for the galaxies in the Local Group and the more massive galaxies in the Local Neighbourhood. We deduce the resulting angular momentum for the whole of the Local Group and…
The conservation law for the angular momentum in curved spacetime, consistent with relativistic quantum mechanics, requires that the antisymmetric part of the affine connection (torsion tensor) is a variable in the principle of least…
Based on the kinetic energy theorem, as one of the fundamental theorems from the classical mechanics, throughout the first part of the article an attempt has been made to derive the mathematical model of a material point motion in the…
We derive an action whose equations of motion contain the Poisson equation of Newtonian gravity. The construction requires a new notion of Newton--Cartan geometry based on an underlying symmetry algebra that differs from the usual Bargmann…
This work explores a classical mechanical theory under two further assumptions: (a) there is a universal dry friction force (Aristotelian mechanics), and (b) the variation of the mass of a body due to wear is proportional to the work done…
The least action principle occupies a central part in contemporary physics. Yet, as far as classical field theory is concerned, it may not be as essential as generally thought. We show with three detailed examples of classical interacting…
Due to Lorentz invariance of General Relativity gravitational interaction is limited to the speed of light. Thus for particles, moving within a matter field, retardation leads to loss of energy by emission of gravitational radiation. This…
The higher derivative gravitational theories exhibit new phenomena absent in General Relativity. One of them is the possible formation of the so called double layer which is the pure gravitational phenomenon and can be interpreted, in a…
We propose a new model of gravity where the Ricci scalar (R) in Einstein-Hilbert action is replaced by an arbitrary function of R and of the norm of energy-momentum tensor i.e., $f(R,T_{\mu\nu}T^{\mu\nu})$. Field equations are derived in…
We investigate particle laws of motion derived from nonstandard kinetic actions of a special form. We are guided by a phenomenological scheme--the modified dynamics (MOND)--that imputes the mass discrepancy observed in galactic systems to a…
It was suggested that observations of the solar system exclude massive gravity, in the sense that the graviton mass must be rigorously zero. This is because there is a discontinuity in the linearized gravity theory at graviton mass equal to…
From a rigorous historic analysis of 1686 I. Newton and 1905 A. Einstein works where the last derived the universal mass-energy relationship, it is concluded that rest mass measures potential energy. From the same formula used to obtain…
A problem of mass in macro- and microcosm has been considered from the single point of view on the basis of the law of conservation of energy. It is shown that in the conservative (absolutely closed) system all types of motion and…