Related papers: A Generalized approach for computing the trajector…
The problem of the existence and uniqueness of the motion of the system of an arbitrary number linear oscillators under a generalized dry-friction type control is studied. This type of control arises in the problem of steering the system to…
The problem of constructing global models describing isolated axially symmetric rotating bodies in equilibrium is analyzed. It is claimed that, whenever the global spacetime is constructed by giving boundary data on the limiting surface of…
The present paper studies the post-Newtonian dynamics of N bodies in general relativity. We derive covariant equations of translational and rotational motion of N extended bodies having arbitrary distribution of mass and velocity of matter…
With the exception of gravitation, the known fundamental interactions of Nature are mediated by gauge fields. A comparison of the candidate groups for a gauge theory possibly describing gravitation favours the Poincar\'e group as the…
We give an overview of the derivation of multipolar equations of motion of extended test bodies for a wide set of gravitational theories beyond the standard general relativistic framework. The classes of theories covered range from simple…
The worldlines (in harmonic coordinates) of two gravitationally interacting massive bodies at the second post-Minkowskian order are described in explicit form. Both the conservative case and the radiation-reacted case are considered. We use…
In the Wigner-covariant rest-frame instant form of dynamics it is possible to develop a relativistic kinematics for the N-body problem. The Wigner hyperplanes define the intrinsic rest frame and realize the separation of the center-of-mass.…
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the relativistic N-body problem in a separable two-body basis in which the particles interact pair-wise through scalar and vector interactions. The resultant N-body…
In this paper, for the spatial Newtonian $2n$-body problem with equal masses, by proving the minimizers of the action functional under certain symmetric, topological and monotone constraints are collision-free, we found a family of spatial…
A surprising "duality" of the Newton equation with time-dependent forces and the stationary Schroedinger equation is discussed. Wide classes of exact solutions not known before for few-body Newton equations are generated directly from…
We consider a bound system of charged particles moving in an external electromagnetic field, including leading relativistic corrections. The difference from the point particle with a magnetic moment comes from the presence of…
We study the problem of motion of a relativistic, ideal elastic solid with free surface boundary by casting the equations in material form ("Lagrangian coordinates"). By applying a basic theorem due to Koch, we prove short-time existence…
The publication of Principia Mathematica in 1678 by Newton became known the celestial bodies motion laws, which characterize the Classical Mechanics. Thereafter made sense to search about the movement of these bodies from known initial…
Why would anyone wish to generalize the already unappetizing subject of rigid body motion to an arbitrary number of dimensions? At first sight, the subject seems to be both repellent and superfluous. The author will try to argue that an…
The motion of a continuum of matter subject to gravitational interaction is classically described by the Euler-Poisson system. Prescribing the density of matter at initial and final times, we are able to obtain weak solutions for this…
Given $n$ point masses turning in a plane at a constant speed, this paper deals with the global bifurcation of periodic solutions for the masses, in that plane and in space. As a special case, one has a complete study of n identical masses…
The looping pendulum is a simple physical system consisting of two masses connected by a string that passes over a rod. We derive equations of motion for the looping pendulum using Newtonian mechanics, and show that these equations can be…
A new hidden variable theory is proposed, according to which particles follows definite trajectories, as in Bohmian Mechanics or Nelson's stochastic mechanics; in the new theory, however, the trajectories are classical, i.e. Newtonian. This…
A method is presented to construct a particular, non-minimally coupled scalar-tensor theory such that a given metric is an exact vacuum solution in that theory. In contrast to the standard approach in studies of gravitational dynamics,…
We investigate static spherically symmetric perfect fluid models in Newtonian gravity for barotropic equations of state that are asymptotically polytropic at low and high pressures. This is done by casting the equations into a 3-dimensional…