Observation Space And Observables In Classical Mechanics
Observation space and observables in classical mechanics.
On a generalization of Helmholtz conditions
Helmholtz conditions in the calculus of variations are necessary and sufficient conditions for a system of differential equations to be variational ‘as it stands’. It is known that this property geometrically means that the dynamical form representing the equations can be completed to a closed form. We study an analogous property for differential forms of degree 3, so-called Helmholtz-type forms in mechanics (), and obtain a generalization of Helmholtz conditions to this case.
On a two-point boundary value problem for second-order differential inclusions on Riemannian manifolds.
On asymptotic motions of robot-manipulator in homogeneous space
In this paper the notion of robot-manipulators in the Euclidean space is generalized to the case in a general homogeneous space with the Lie group of motions. Some kinematic subspaces of the Lie algebra (the subspaces of velocity operators, of Coriolis acceleration operators, asymptotic subspaces) are introduced and by them asymptotic and geodesic motions are described.
On Carnot's theorem in time dependent impulsive mechanics.
We show that the validity of the Carnot's theorem about the kinetic energy balance for a mechanical system subject to an inert impulsive kinetic constraint, once correctly framed in the time dependent geometric environment for Impulsive Mechanics given by the left and right jet bundles of the space-time bundle N, is strictly related to the frame of reference used to describe the system and then it is not an intrinsic property of the mechanical system itself. We analyze in details the class of frames...
On differential inclusions of velocity hodograph type with Carathéodory conditions on Riemannian manifolds
We investigate velocity hodograph inclusions for the case of right-hand sides satisfying upper Carathéodory conditions. As an application we obtain an existence theorem for a boundary value problem for second-order differential inclusions on complete Riemannian manifolds with Carathéodory right-hand sides.
On Galilean connections and the first jet bundle
We see how the first jet bundle of curves into affine space can be realized as a homogeneous space of the Galilean group. Cartan connections with this model are precisely the geometric structure of second-order ordinary differential equations under time-preserving transformations - sometimes called KCC-theory. With certain regularity conditions, we show that any such Cartan connection induces “laboratory” coordinate systems, and the geodesic equations in this coordinates form a system of second-order...
On integration factor of a dynamical system.
On some cohomological properties of the Lie algebra of Euclidean motions
The external derivative on differential manifolds inspires graded operators on complexes of spaces , , stated by dual to a Lie algebra . Cohomological properties of these operators are studied in the case of the Lie algebra of the Lie group of Euclidean motions.
On the existence of equations of evolution.
On the geometry and behavior of -body motions.
On the principle of stability of invariance of physical systems
On the question of stability in a Hamiltonian system
Orbitas Frenadas En Sistemas Mecanicos Finslerianos.
Orbites périodiques de systèmes conservatifs