Related papers: The principle of least action for test particles i…
When addressing spatial biological questions using mathematical models, symmetries within the system are often exploited to simplify the problem by reducing its physical dimension. In a reduced-dimension model molecular movement is…
As V. I. Arnold observed in the 1960s, the Euler equations of incompressible fluid flow correspond formally to geodesic equations in a group of volume-preserving diffeomorphisms. Working in an Eulerian framework, we study incompressible…
We present an action principle formulation for the study of motion of an extended body in General Relativity in the limit of weak gravitational field. This gives the classical equations of motion for multipole moments of arbitrary order…
The possibility of geometrization of the gravitational and electro magnetic fields in 4D Finsler space (the Model of Embedded Spaces -- MES) is investigated. The model postulates a proper metric set of an element of distributed matter and…
We consider the motion of spinning test particles with nonzero rest mass in the "pole-dipole" approximation, as described by the Mathisson-Papapetrou-Dixon (MPD) equations, and examine its properties in dependence on the spin supplementary…
In this paper, we derive from the principle of least action the equation of motion for a continuous medium with regularized density field in the context of measures. The eventual equation of motion depends on the order in which…
In this paper we have resolved the apparent paradox of different mechanical equations for force and torque governing the motion of a charged particle in different inertial frames. The same paradox arises in all usual ``explanations'' of the…
There is a vast literature showing the connection between a deformed relativistic kinematics and a curved momentum space, and, in particular, how the former can be obtained from the geometrical properties of the latter. However, there is…
We consider the compatibility of the equations of motion which follow from d'Alembert's principle in the case of a general autonomous non-holonomic mechanical system in N dimensions, with those equations which follow for the same system by…
A variational principle is applied to 4D Euclidean space provided with a tensor refractive index, defining what can be seen as 4-dimensional optics (4DO). The geometry of such space is analysed, making no physical assumptions of any kind.…
It is shown that for a relativistic particle moving in an electromagnetic field its equations of motion written in a form of the second law of Newton can be reduced with the help of elementary operations to the Hamilton-Jacobi equation. The…
It is pointed out that the current form of extrinsic equation of motion for a particle constrained to remain on a hypersurface is in fact a half-finished version for it is established without regard to the fact that the particle can never…
The existence of chaotic behavior for the geodesics of the test particles orbiting compact objects is a subject of much current research. Some years ago, Gu\'eron and Letelier [Phys. Rev. E \textbf{66}, 046611 (2002)] reported the existence…
To accomplish a task within limited operation time typically requires an excess expense of energy, whose minimum is of practical importance for the optimal design in various applications, especially in the industrial separation of mixtures…
We discuss the leading order correction to the equation of motion of a particle with spin on an arbitrary spacetime. A particle traveling in a curved spacetime is known to trace a geodesic of the background spacetime if the mass of the…
The noncommutative spectral action extends our familiar notion of commutative spaces, using the data encoded in a spectral triple on an almost commutative space. Varying a rather simple action, one can derive all of the standard model of…
The lecture explains the geometric basis for the recently-discovered nonholonomic mapping principle which specifies certain laws of nature in spacetimes with curvature and torsion from those in flat spacetime, thus replacing and extending…
It is proposed the generalized action functional for N=1 superparticle in D=3,4,6 and 10 space-time dimensions. The superfield geometric approach equations describing superparticle motion in terms of extrinsic geometry of the worldline…
We extend our previous calculation of the quasi-local contribution to the self-force on a scalar particle to general (not necessarily geodesic) motion in a general spacetime. In addition to the general case and the case of a particle at…
We propose gravity, matters and dark energy may be confined on different four dimensional \emph{minimal surfaces} for the observer in five dimensional spacetime. Following this idea, we construct the equations of motion when gravity,…