On a horizontal structure on differentiable manifolds
On a “mysterious” case of a quadratic Hamiltonian.
On a simulation of the oscillation excited by a random force
On a Trace Functional for Formal Pseudo-Differential Operators and the Symplectic Structure of the Korteweg-Devries Type Equation.
On a two-point boundary value problem for second-order differential inclusions on Riemannian manifolds.
On a variational approach to optimization of hybrid mechanical systems.
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 Axiomatic Foundations Common to Classical Physics and Special Relativity
(i) The class of the axiomatic foundations mentioned in the title is called Ax Found; and its structure is treated in the introduction. (ii) This consists of Parts A to G followed by the References. (iii) In [17] Bressan's modal logic is treated in a consciously non-rigorous way. Instead here, as well as Ax Found, it has a rigorous treatment. Such a treatment had been appreciated by the mathematical physicist C. Truesdell in [62]. (iv) In 1953 Truesdell had a remarkable...
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 central configurations.
On classical dynamics of affinely-rigid bodies subject to the Kirchhoff-Love constraints.
On classical intrinsically resonant formal perturbation theory
On classical -matrix for the Kowalevski gyrostat on .
On control problems of minimum time for Lagrangian systems similar to a swing. I. Convexity criteria for sets
One establishes some convexity criteria for sets in . They will be applied in a further Note to treat the existence of solutions to minimum time problems for certain Lagrangian systems referred to two coordinates, one of which is used as a control. These problems regard the swing or the ski.
On control problems of minimum time for Lagrangian systems similar to a swing. II Application of convexity criteria to certain minimum time problems
This Note is the Part II of a previous Note with the same title. One refers to holonomic systems with two degrees of freedom, where the part can schemetize a swing or a pair of skis and schemetizes whom uses . The behaviour of is characterized by a coordinate used as a control. Frictions and air resistance are neglected. One considers on minimum time problems and one is interested in the existence of solutions. To this aim one determines a certain structural condition which implies...
On control theory and its applications to certain problems for Lagrangian systems. On hyperimpulsive motions for these. II. Some purely mathematical considerations for hyper-impulsive motions. Applications to Lagrangian systems
See Summary in Note I. First, on the basis of some results in [2] or [5]-such as Lemmas 8.1 and 10.1-the general (mathematical) theorems on controllizability proved in Note I are quickly applied to (mechanic) Lagrangian systems. Second, in case , and satisfy conditions (11.7) when is a polynomial in , conditions (C)-i.e. (11.8) and (11.7) with -are proved to be necessary for treating satisfactorily 's hyper-impulsive motions (in which positions can suffer first order discontinuities)....
On control theory and its applications to certain problems for Lagrangian systems. On hyper-impulsive motions for these. III. Strengthening of the characterizations performed in parts I and II, for Lagrangian systems. An invariance property.
In [1] I and II various equivalence theorems are proved; e.g. an ODE with a scalar control is linear w.r.t. iff its solution with given initial conditions (chosen arbitrarily) is continuous w.r.t. in a certain sense, or iff
On D’Alembert’s Principle
A formulation of the D’Alembert principle as the orthogonal projection of the acceleration onto an affine plane determined by nonlinear nonholonomic constraints is given. Consequences of this formulation for the equations of motion are discussed in the context of several examples, together with the attendant singular reduction theory.
On decomposability of Nambu-Poisson tensor.
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.