Related papers: Lectures on the free period Lagrangian action func…
We explore the classical dynamics of two interacting rotating dipoles that are fixed in the space and exposed to an external homogeneous electric field. Kinetic energy transfer mechanisms between the dipoles are investigated varying both…
We prove the existence of periodic bounce orbits of prescribed energy on an open bounded domain in Euclidean space. We derive explicit bounds on the period and the number of bounce points.
The orbits about Lagrangian equilibrium points are important for scientific investigations. Since, a number of space missions have been completed and some are being proposed by various space agencies. In light of this, we consider a more…
Multiplicity results for solutions of various boundary value problems are known for dynamical systems on compact configuration manifolds, given by Lagrangians or Hamiltonians which have quadratic growth in the velocities or in the momenta.…
We prove that, on a closed surface, a Lagrangian system defined by a Tonelli Lagrangian $L$ possesses a periodic orbit that is a local minimizer of the free-period action functional on every energy level belonging to the low range of…
Some models allowing explicit calculation of periodic instantons and evaluation of their action are studied with regard to transitions from classical to quantum behaviour as the temperature is lowered and tunneling sets in. It is shown that…
Symmetries are ubiquitous in a wide range of nonlinear systems. Particularly in systems whose dynamics are determined by a Lagrangian or Hamiltonian function. For hybrid systems which possess a continuous-time dynamics determined by a…
In this work the existence of periodic solutions is studied for the Hamiltonian functions (Formula presented.) where the first term consist of a harmonic oscillator and the second term are homogeneous polynomials of degree 5 defined by two…
In this work, we propose a method for calculating the free energy of anisotropic classical spin systems. We use a Hubbard-Stratonovich transformation to express the partition function of a generic bilinear super-exchange Hamiltonian in…
The paper analyzes a Lagrangian system which is controlled by directly assigning some of the coordinates as functions of time, by means of frictionless constraints. In a natural system of coordinates, the equations of motions contain terms…
Unfortunately, the Hamiltonian mechanics of degenerate Lagrangian systems is usually presented as a mere recipe of Dirac, with no explanation as to how it works. Then it comes to discussing conjectures of whether all primary constraints…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
For Hamiltonian flows we establish the existence of periodic orbits on a sequence of level sets approaching a Bott-nondegenerate symplectic extremum of the Hamiltonian. As a consequence, we show that a charge on a compact manifold with a…
The complexity of arbitrary dynamical systems and chemical reactions, in particular, can often be resolved if only the appropriate periodic orbit - in the form of a limit cycle, dividing surface, instanton trajectories or some other related…
A Lagrangian system with two degrees of freedom is considered. The configuration space of the system is a cylinder. A large class of periodic solutions has been found. The solutions are not homotopy equivalent to each other.
We seek frozen planet orbits for the helium atom through an application of the Mountain Pass Lemma to the Lagrangian action functional. Our method applies to a wide class of gravitational-like interaction potentials thus generalising the…
We present an illustrative application of the two famous mathematical theorems in differential topology in order to show the existence of periodic orbits with arbitrary given period for a class of hamiltonians .This result point out for a…
We analyze a new class of time-periodic nonreciprocal dynamics in interacting chaotic classical spin systems, whose equations of motion are conservative (phase-space-volume-preserving) yet possess no symplectic structure. As a result, the…
In this paper we produce a lower bound for the number of periodic orbits of certain Hamiltonian vector fields near Bott-nondegenerate symplectic critical submanifolds. This result is then related to the problem of finding closed orbits of…
In the present work, we study the classical behavior of an electric dipole in presence of an external uniform magnetic field. We derive equations and constants of motion from the Lagrangian formulation. We obtain an infinitely periodic…