Related papers: Problem of Metrizability for the Dynamical Systems…
The behavior of dynamical system interacting with non-equilibrium medium is investigated. Formally exact kinetic equations are derived for the statistical operator of the dynamical system and the macroscopic parameters of the medium. In the…
Modified Newtonian dynamics can be considered as an effect derived from a squeezable extra dimension space. The third law of Newtonian dynamics can be managed to remain valid in the 5-space. The critical acceleration parameter $a_0$ appears…
We propose a representation for the set of forces a robot can counteract using full system dynamics: the residual force polytope. Given the nominal torques required by a dynamic motion, this representation models the forces which can be…
We determine the complete space-time metric from the bootstrapped Newtonian potential generated by a static spherically symmetric source in the surrounding vacuum. This metric contains post-Newtonian parameters which can be further used to…
Controlling hybrid systems is mostly very challenging due to the variety of dynamics these systems can exhibit. Inspired by the concept of differential flatness of nonlinear continuous systems and their inherent invertibility property, the…
This paper proposes a tractable framework to determine key characteristics of non-linear dynamic systems by converting physics-informed neural networks to a mixed integer linear program. Our focus is on power system applications.…
We study the problem of relaxing a large cosmological constant in the astrophysical domain through a dynamical mechanism based on a modified action of gravity previously considered by us at the cosmological level. We solve the model in the…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
The nonequilibrium thermodynamics of an open (classical or quantum) system in strong contact with a single heat bath can be conveniently described in terms of the Hamiltonian of mean force. However, the conventional formulation is limited…
The behavior of any physical system is governed by its underlying dynamical equations. Much of physics is concerned with discovering these dynamical equations and understanding their consequences. In this work, we show that, remarkably,…
A modified-gravity-type model of two hypothetical massless vector fields is presented. These vector fields are gravitationally coupled to standard matter and an effective cosmological constant. Considered in a cosmological context, the…
If $F:H\to H$ is a map in a Hilbert space $H$, $F\in C^2_{loc}$, and there exists $y$, such that $F(y)=0$, $F'(y)\not= 0$, then equation $F(u)=0$ can be solved by a DSM (dynamical systems method). This method yields also a convergent…
Soft robotic manipulators provide numerous advantages over conventional rigid manipulators in fragile environments such as the marine environment. However, developing analytic inverse models necessary for shape, motion, and force control of…
We have tested a previous analytical estimate of the dynamical friction timescale in Modified Newtonian Dynamics (MOND) with fully non-linear N-body simulations. The simulations confirm that the dynamical friction timescale is significantly…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
Motivated by a class of orbit problems in astrophysics, this paper considers solutions to Hill's equation with forcing strength parameters that vary from cycle to cycle. The results are generalized to include period variations from cycle to…
The Classical Newtonian problem of describing the free motions of N gravitating bodies which form an isolated system in free space has been considered. It is well known from the Poincares Dictum that the problem is not exactly solvable.…
Recently, Anderson et al. published an empirical prediction formula for the so far unexplained parts of the velocity changes of spacecrafts during Earth flybys. In the framework of a perturbational approach, we show that there is no…
Active motion is a concept in complex systems theory and was successfully applied to various problems in nonlinear dynamics. Explicit studies for gravitational potentials were missing so far. We interpret the Friedmann equations with…
Electromagnetic fields which solve the vacuum Maxwell equations in one spacetime are well-known to also be solutions in all spacetimes with conformally-related metrics. This provides a sense in which electromagnetism alone cannot be used to…