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.
On the multiplicity of brake orbits and homoclinics in Riemannian manifolds
Let be a complete Riemannian manifold, an open subset whose closure is diffeomorphic to an annulus. If is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in starting orthogonally to one connected component of and arriving orthogonally onto the other one. The results given in [5] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating...
On the nature of time.
On the notion of Jacobi fields in constrained calculus of variations
In variational calculus, the minimality of a given functional under arbitrary deformations with fixed end-points is established through an analysis of the so called second variation. In this paper, the argument is examined in the context of constrained variational calculus, assuming piecewise differentiable extremals, commonly referred to as extremaloids. The approach relies on the existence of a fully covariant representation of the second variation of the action functional, based on a family of...
On the principle of stability of invariance of physical systems
On the Principle of Stationary Isoenergetic Action
On the problem of stability for near to integrable Hamiltonian systems.
On the question of stability in a Hamiltonian system
On the real singularities of the N-body problem.