相关论文: On Periodic Solutions to Some Lagrangian System Wi…
A Lagrangian system with singularities is considered. The configuration space is a non-compact manifold that depends on time. A set of periodic solutions has been found.
In this paper we provide a sufficient condition for the linear instability of a periodic orbit for a free period Lagrangian system on a Riemannian manifold. The main result establish a general criterion for the linear instability of a maybe…
Some characteristics of the Sawada-Kotera Lagrangian system lend themselves to generalization, producing a large class of separable Lagrangian systems with two degrees of freedom.
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…
A geometric global formulation of the higher-order Lagrangian formalism for systems with finite number of degrees of freedom is provided. The formalism is applied to the study of systems with groups of Noetherian symmetries.
We construct solutions of analogues of the nonstationary Schr\"odinger equation corresponding to the polynomial isomonodromic Hamiltonian Garnier system with two degrees of freedom. This solutions are obtained from solutions of systems of…
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…
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…
Free coherent states for a system with two degrees of freedom is defined. An isomorphism of the space of distributions on 2-adic disc and the space of free coherent states is constructed.
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…
In this paper, we will consider a kind of infinite dimensional Hamiltonian system(HS), by the method of saddle point reduction, topology degree and the index, we will get the existence of periodic solution for (HS).
In this paper we present a Lagrangian method that allows the physical degree of freedom count for any Lagrangian system without having to perform neither Dirac nor covariant canonical analyses. The essence of our method is to establish a…
For a class of polynomial non-autonomous differential equations of degree n, we use phase plane analysis to show that each equation in this class has n periodic solutions. The result implies that certain rigid two-dimensional systems have…
For positive definite Lagrange systems with two degrees of freedom, it is a typical phenomenon that all minimal periodic orbits are hyperbolic.
We show that well-chosen Lagrangians for a class of two-dimensional integrable lattice equations obey a closure relation when embedded in a higher dimensional lattice. On the basis of this property we formulate a Lagrangian description for…
We consider the question of counting the degrees of freedom in theoretical models, with an emphasis on theories of fields and gravity. Among the possible approaches, the Hamiltonian formulation remains one of the most systematic and robust…
We present the capability of Lagrangian descriptors for revealing the high dimensional phase space structures that are of interest in nonlinear Hamiltonian systems with index-1 saddle. These phase space structures include normally…
A gauge independent method of obtaining the reduced space of constrained dynamical systems is discussed in a purely lagrangian formalism. Implications of gauge fixing are also considered.
This paper is concerned with the following Euler-Lagrange system \[ \frac{d}{dt}\mathcal{L}_v(t,u(t),\dot u(t))=\mathcal{L}_x(t,u(t),\dot u(t))\quad \text{ for a.e. }t\in[-T,T],\quad u(-T)=u(T), \] where Lagrangian is given by…
It is shown that a given non-autonomous system of two first-order ordinary differential equations can be expressed in Hamiltonian form. The derivation presented here allow us to obtain previously known results such as the infinite number of…