Related papers: Questioning Newton's second law: What is the struc…
Dynamics of systems of structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. 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…
The action principle is frequently used to derive the classical equations of motion. The action may also be used to associate group elements with curves in the space-time manifold, similar to the gauge transformations. The action principle…
Newtonian dynamics is derived from prior information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the state of a particle is defined by…
Newton's second law: "force = time-derivative of momentum", may also be defined for theories of gravitation endowing space-time with a curved metric. Thus, Einstein's assumption of a geodesic motion may be rewritten in that form, and it…
The basic physics disciplines of Maxwell's electrodynamics and Newton's mechanics have been thoroughly tested in the laboratory, but they can nevertheless also support nonphysical solutions. The unphysical nature of some dynamical…
The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order…
This article serves as a pedagogical introduction to the problem of motion in classical field theories. The primary focus is on self-interaction: How does an object's own field affect its motion? General laws governing the self-force and…
We start by formulating geometrically the Newton's law for a classical free particle in terms of Riemannian geometry, as pattern for subsequent developments. In fact, we use this scheme for further generalisation devoted to a constrained…
A discrete system constituted of particles interacting by means of a centroid-based law is numerically investigated. The elements of the system move in the plane, and the range of the interaction can be varied from a more local form…
When a small, uncharged, compact object is immersed in an external background spacetime, at zeroth order in its mass it moves as a test particle in the background. At linear order, its own gravitational field alters the geometry around it,…
In teaching the physical sciences, a significant challenge lies in the student's tendency to consider the scientific world and the "real" world as separate. For example, Newton's 1st Law of Motion states that an object in motion remains in…
The construction of a gauge field theory for elementary particles usually starts by promoting global invariance of the matter action to a local one, this in turn implying the introduction of gauge fields. We present here a procedure that…
Using a rigorous method of matched asymptotic expansions, I derive the equation of motion of a small, compact body in an external vacuum spacetime through second order in the body's mass (neglecting effects of internal structure). The…
Riemann's principle "force equals geometry" provided the basis for Einstein's General Relativity - the geometric theory of gravitation. In this paper, we follow this principle to derive the dynamics for any static, conservative force. The…
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,…
It is well known that the equations of motion obtained from Newtons second law of motion can be obtained from a Lagrangian via the Euler-Lagrangian formulation if and only if the equations of motion satisfy the Helmholtz conditions. In this…
Along the general framework of the gauge-invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. {\bf 110} (2003), 723; {\it ibid}, {\bf 113} (2005), 481.], we re-derive the second-order Einstein equations on…
It is shown that all possible gravitational, gauge and other interactions experienced by particles in ordinary d-dimensions (one-time) can be described in the language of two-time physics in a spacetime with d+2 dimensions. This is obtained…
Starting from the classical Newton's second law which, according to our assumption, is valid in any instantaneous inertial rest frame of body that moves in Minkowskian space-time we get the relativistic equation of motion…