A new geometrical framework for time-dependent Hamiltonian mechanics.
A new Lagrangian dynamic reduction in field theory
For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first jet bundle of a principal bundle. It is shown that covariant and dynamic reduction lead to equivalent equations of motion. This is achieved by constructing a new Lagrangian defined on an infinite dimensional space which turns out to be gauge group invariant.
A new look at classical mechanics of constrained systems
A new method for measuring the splitting of invariant manifolds
A note on a connection between the Poincaré-Arnold-Melnikov integral and the Picard-Vessiot theory
We obtain an algebraic interpretation by means of the Picard-Vessiot theory of a result by Ziglin about the self-intersection of complex separatrices of time-periodically perturbed one-degree of freedom complex analytical Hamiltonian systems.
A note on an approximative scheme of finding almost homoclinic solutions for Newtonian systems
In this work we will be concerned with the existence of almost homoclinic solutions for a Newtonian system , where t ∈ ℝ, q ∈ ℝⁿ. It is assumed that a potential V: ℝ × ℝⁿ → ℝ is C¹-smooth and its gradient map is bounded with respect to t. Moreover, a forcing term f: ℝ → ℝⁿ is continuous, bounded and square integrable. We will show that the approximative scheme due to J. Janczewska (see [J2]) for a time periodic potential extends to our case.
A note on generic chaos
We consider dynamical systems on a separable metric space containing at least two points. It is proved that weak topological mixing implies generic chaos, but the converse is false. As an application, some results of Piórek are simply reproved.
A Note on Shock Profiles in Dissipative Hyperbolic and Parabolic Models
A note on the rotationally symmetric SO(4) Euler rigid body.
A proof of universality of arc length as time parameter in Kepler problems.
A property of connections of mechanical systems of higher order
A quantum particle in a quadrupole radio-frequency trap
A realistic exponential estimate for a paradigm hamiltonian
A recursive scheme of first integrals of the geodesic flow of a Finsler manifold.
A remarkable periodic solution of the three-body problem in the case of equal masses.
A sequence adapted from the movement of the center of mass of two planets in solar system
In this paper we derive a sequence from a movement of center of~mass of arbitrary two planets in some solar system, where the planets circle on concentric circles in a same plane. A trajectory of center of mass of the planets is discussed. A sequence of points on the trajectory is chosen. Distances of the points to the origin are calculated and a distribution function of a sequence of the distances is found.
A simple trolley-like model in the presence of a nonlinear friction and a bounded fuel expenditure
We consider a problem of maximization of the distance traveled by a material point in the presence of a nonlinear friction under a bounded thrust and fuel expenditure. Using the maximum principle we obtain the form of optimal control and establish conditions under which it contains a singular subarc. This problem seems to be the simplest one having a mechanical sense in which singular subarcs appear in a nontrivial way.
A singular lagrangian model for N-body relativistic interactions
A special nonlinear connection in second order geometry.
A stability criterion for periodic systems with first integrals