Related papers: Numerical Studies of Hamiltonian Systems and Appli…
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic…
In previous work, we have considered Hamiltonians associated with 3 dimensional conformally flat spaces, possessing 2, 3 and 4 dimensional isometry algebras. Previously our Hamiltonians have represented free motion, but here we consider the…
Numerical methods play an ever more important role in astrophysics. This is especially true in theoretical works, but of course, even in purely observational projects, data analysis without massive use of computational methods has become…
These lectures are intended to provide an introduction to the rich interplay between N-body simulations and stellar-kinematic observations of galaxies. The first section describes the kinematic properties of galaxies that are accessible to…
The path probability of stochastic motion of non dissipative or quasi-Hamiltonian systems is investigated by numerical experiment. The simulation model generates ideal one-dimensional motion of particles subject only to conservative forces…
Invariant manifolds are the skeleton of the chaotic dynamics in Hamiltonian systems. In Celestial Mechanics, for instance, these geometrical structures are applied to a multitude of physical and practical problems, such as to the…
The dynamics of a three-dimensional Hamilton-Poisson system is closely related to its constants of motion, the energy or Hamiltonian function $H$ and a Casimir $C$ of the corresponding Lie algebra. The orbits of the system are included in…
We present a Hamiltonian approach for the wellknown Eigen model of the Darwin selection dynamics. Hamiltonization is carried out by means of the embedding of the population variable space, describing behavior of the system, into the space…
We analyze infinite-dimensional Hamiltonian systems corresponding to partial differential equations on one-dimensional spatial domains formulated with formally skew-adjoint Hamiltonian operators and nonlinear Hamiltonian density. In various…
We examine the problem of integrability of two-dimensional Hamiltonian systems by means of separation of variables. The systematic approach to construction of the special non-pure coordinate separation of variables for certain natural…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
The Galilean satellites' dynamics has been studied extensively during the last century. In the past it was common to use analytical expansions in order to get simple models to integrate, but with the new generation computers it became…
Hamiltonian dynamics can be used to produce distant proposals for the Metropolis algorithm, thereby avoiding the slow exploration of the state space that results from the diffusive behaviour of simple random-walk proposals. Though…
The H\'enon-Heiles system, initially introduced as a simplified model of galactic dynamics, has become a paradigmatic example in the study of nonlinear systems. Despite its simplicity, it exhibits remarkably rich dynamical behavior,…
In this paper we investigate a class of natural Hamiltonian systems with two degrees of freedom. The kinetic energy depends on coordinates but the system is homogeneous. Thanks to this property it admits, in a general case, a particular…
These are pedagogical notes on the Hamiltonian formulation of constrained dynamical systems. All the examples are finite dimensional, field theories are not covered, and the notes could be used by students for a preliminary study before the…
The Nelson model describes the interaction of nonrelativistic quantum particles with a relativistic quantum field of scalar bosons. Nelson rigorously demonstrated in 1964 the existence of a well-defined self-adjoint Nelson Hamiltonian by…
We consider a restricted four-body problem on the dynamics of a massless particle under the gravitational force produced by three mass points forming an equilateral triangle configuration. We assume that the mass m3 of one primary is very…
Computational gas dynamics has become a prominent research field both in astrophysics and cosmology. In the first part of this review we intend to briefly describe several of the numerical methods used in this field, discuss their range of…