On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation
On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation
We present the semi-conductor Boltzmann equation, which is time-reversible, and indicate that it can be formally derived by considering the large time and small perturbing potential limit in the Von-Neumann equation (time-reversible). We then rigorously compute the corresponding asymptotics in the case of the Von-Neumann equation on the Torus. We show that the limiting equation we obtain does not coincide with the physically realistic model. The former is indeed an equation of Boltzmann type, yet...
On the determination of the potential function from given orbits
The paper deals with the problem of finding the field of force that generates a given ()-parametric family of orbits for a mechanical system with degrees of freedom. This problem is usually referred to as the inverse problem of dynamics. We study this problem in relation to the problems of celestial mechanics. We state and solve a generalization of the Dainelli and Joukovski problem and propose a new approach to solve the inverse Suslov’s problem. We apply the obtained results to generalize the...
On the differential equations of the classical and relativistic dynamics for certain generalised Lagrangian functions
One studies the differential equations of the movement of certain classical and relativistic systems for some special Lagrangian functions. One considers particularly the case in which the problem presents cyclic coordinates. Some electrodynamical applications are studied.
On the dynamics of a nonlinear multidimensional oscillator with memory.
On the evection resonance and its connection to the stability of outer satellites.
On the existence and non-existence of closed trajectories for some Hamiltonian flows.
On the existence of equations of evolution.
On the generalized Lagrange spaces associated to the remarkable Lagrangians.
On the geometry and behavior of -body motions.
On the higher order Poincaré-Cartan forms
On the Integral Manifolds of the N-Body Problem.
On the inverse problem of the calculus of variations for ordinary differential equations
Lepagean 2-form as a globally defined, closed counterpart of higher-order variational equations on fibered manifolds over one-dimensional bases is introduced, and elementary proofs of the basic theorems concerning the inverse problem of the calculus of variations, based on the notion of Lepagean 2-form and its properties, are given.
On the inverse variational problem in nonholonomic mechanics
The inverse problem of the calculus of variations in a nonholonomic setting is studied. The concept of constraint variationality is introduced on the basis of a recently discovered nonholonomic variational principle. Variational properties of first order mechanical systems with general nonholonomic constraints are studied. It is shown that constraint variationality is equivalent with the existence of a closed representative in the class of 2-forms determining the nonholonomic system. Together with...
On the Isoenergetical Non-Degeneracy of the Problem of two Centers of Gravitation
* Partialy supported by contract MM 523/95 with Ministry of Science and Technologies of Republic of Bulgaria.For the system describing the motion of a moss point under the action of two static gravity centers (with equal masses), we find a subset of the set of the regular values of the energy and momentum, where the condition of isoenergetical non-degeneracy is fulfilled.
On the KAM - Theory Conditions for the Kirchhoff Top
* Partially supported by Grant MM523/95 with Ministry of Science and Technologies.In this paper the classical Kirchhoff case of motion of a rigid body in an infinite ideal fluid is considered. Then for the corresponding Hamiltonian system on the zero integral level, the KAM theory conditions are checked. In contrast to the known similar results, there exists a curve in the bifurcation diagram along which the Kolmogorov’s condition vanishes for certain values of the parameters.
On the Lagrange-Souriau form in classical field theory
The Euler-Lagrange equations are given in a geometrized framework using a differential form related to the Poincare-Cartan form. This new differential form is intrinsically characterized; the present approach does not suppose a distinction between the field and the space-time variables (i.e. a fibration). In connection with this problem we give another proof describing the most general Lagrangian leading to identically vanishing Euler-Lagrange equations. This gives the possibility to have a geometric...
On the linearization of second-order differential and difference equations.
On the mechanics with noncontinuous hamiltonians
On the mobility and efficiency of mechanical systems
It is shown that self-locomotion is possible for a body in Euclidian space, provided its dynamics corresponds to a non-quadratic Hamiltonian, and that the body contains at least 3 particles. The efficiency of the driver of such a system is defined. The existence of an optimal (most efficient) driver is proved.