Related papers: An angular-momentum preserving dissipative model f…
This work investigates different models of rotational dynamics of two rigid bodies with the shape of an ellipsoid, moving under their gravitational influence. The focus of this study is on their behavior, their linear stability, and…
We employ a port-Hamiltonian approach to model nonlinear rigid multibody systems subject to both position and velocity constraints. Our formulation accommodates Cartesian and redundant coordinates, respectively, and captures kinematic as…
Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…
The concept of grand angular momentum is widely used in the study of N-body problems quantum mechanically. Here, we applied it to a classical analysis of N-body problems. Utilizing the tree representation for Jacobi and hyperspherical…
We introduce an energy-based model, which seems especially suited for constrained systems. The proposed model provides an alternative to the popular port-Hamiltonian framework and exhibits similar properties such as energy dissipation as…
Recently, Morrison and Updike showed that many dissipative systems are naturally described as possessing a Riemann curvature-like bracket, which similar to the Poisson bracket, generates the dissipative equations of motion once suitable…
We show that discreteness effects related to classical two-body relaxation produce spurious heating of the gaseous component in numerical simulations of galaxy formation. A simple analytic model demonstrates that this artificial heating…
In this work, which is based on an essential linear analysis carried out by Christodoulou, we study the evolution of tidal energy for the motion of two gravitating incompressible fluid balls with free boundaries obeying the Euler-Poisson…
We revisit the two body problem, where one body can be deformed under the action of tides raised by the companion. Tidal deformation and consequent dissipation result in spin and orbital evolution of the system. In general, the equations of…
One of the fundamental aspects of statistical behaviour in many-body systems is exponential divergence of neighbouring orbits, which is often discussed in terms of Liapounov exponents. Here we study this topic for the classical…
We consider the solid-solid interactions in the two body problem. The relative equilibria have been previously studied analytically and general motions were numerically analyzed using some expansion of the gravitational potential up to the…
We perform the bifurcation analysis of the Kepler problem on $S^3$ and $L^3$. An analogue of the Delaunay variables is introduced. We investigate the motion of a point mass in the field of the Newtonian center moving along a geodesic on…
We investigate discretization strategies for a recently introduced class of energy-based models. The model class encompasses classical port-Hamiltonian systems, generalized gradient flows, and certain systems with algebraic constraints. Our…
This article aims to derive equations of motion for dynamical systems with angular momentum on Finsler geometries. To this end, we apply Souriau's Principle of General Covariance, which is a geometrical framework to derive diffeomorphism…
We present a tidal model for treating the rotational evolution in the general three-body problem with arbitrary viscosities, in which all the masses are considered to be extended and all the tidal interactions between pairs are taken into…
We study the stability of the circular orbits of the electromagnetic two-body problem of classical electrodynamics. We introduce the concept of resonant dissipation, i.e. a motion that radiates the center-of-mass energy while the…
From Hamilton's principle of stationary action, we derive governing equations of two-fluid mixtures and extend the model to the dissipative case without chemical reactions. For both conservative and dissipative cases, an algebraic identity…
We study by means of numerical simulations the model of dissipative particle dynamics with energy conservation for the simple case of thermal conduction. It is shown that the model displays correct equilibrium fluctuations and reproduces…
We show that during normal modes of an oscillatory system consisting of a hoop and a cylinder joining their centers by an ideal spring, its central mass does not remain at rest. This effect is due to the resultant external static friction…