Alcuni teoremi di cinematica dei sistemi rigidi
Algebraic calculation of the energy eigenvalues for the nondegenerate three-dimensional Kepler-Coulomb potential.
Algebraically completely integrable systems and Kummer varieties.
Algebras of integrals
Algèbres de Lie, systèmes hamiltoniens, courbes algébriques
Algebro-geometric Integration in Classical and Statistical Mechanics
Almost product structures and Poisson reduction of presymplectic systems.
Alternative transfers to the NEOs 99942 apophis, 1994 WR12, and 2007 UW1 via derived trajectories from periodic orbits of family G.
An affine framework for analytical mechanics
An affine Cartan calculus is developed. The concepts of special affine bundles and special affine duality are introduced. The canonical isomorphisms, fundamental for Lagrangian and Hamiltonian formulations of the dynamics in the affine setting are proved.
An algorithm based on rolling to generate smooth interpolating curves on ellipsoids
We present an algorithm to generate a smooth curve interpolating a set of data on an -dimensional ellipsoid, which is given in closed form. This is inspired by an algorithm based on a rolling and wrapping technique, described in [11] for data on a general manifold embedded in Euclidean space. Since the ellipsoid can be embedded in an Euclidean space, this algorithm can be implemented, at least theoretically. However, one of the basic steps of that algorithm consists in rolling the ellipsoid, over...
An alternative canonical approach to the ghost problem in a complexified extension of the Pais-Uhlenbeck oscillator.
An alternative proof of Painlevé's theorem
In this article we show some aspects of analytical and numerical solution of the -body problem, which arises from the classical Newtonian model for gravitation attraction. We prove the non-existence of stationary solutions and give an alternative proof for Painlevé’s theorem.
An analysis of the boundary layer in the 1D surface Cauchy–Born model
The surface Cauchy–Born (SCB) method is a computational multi-scale method for the simulation of surface-dominated crystalline materials. We present an error analysis of the SCB method, focused on the role of surface relaxation. In a linearized 1D model we show that the error committed by the SCB method is 𝒪(1) in the mesh size; however, we are able to identify an alternative “approximation parameter” – the stiffness of the interaction potential – with respect to which the relative error...
An analysis of the boundary layer in the 1D surface Cauchy–Born model∗
The surface Cauchy–Born (SCB) method is a computational multi-scale method for the simulation of surface-dominated crystalline materials. We present an error analysis of the SCB method, focused on the role of surface relaxation. In a linearized 1D model we show that the error committed by the SCB method is 𝒪(1) in the mesh size; however, we are able to identify an alternative “approximation parameter” – the stiffness of the interaction potential – with respect to which the relative error...
An analysis of the effect of ghost force oscillation on quasicontinuum error
The atomistic to continuum interface for quasicontinuum energies exhibits nonzero forces under uniform strain that have been called ghost forces. In this paper, we prove for a linearization of a one-dimensional quasicontinuum energy around a uniform strain that the effect of the ghost forces on the displacement nearly cancels and has a small effect on the error away from the interface. We give optimal order error estimates that show that the quasicontinuum displacement converges to the atomistic...
An analytical and numerical approach to a bilateral contact problem with nonmonotone friction
We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The first approach...
An Elementary Treatise on Quaternions [Book]
An energy conserving modification of numerical methods for the integration of equations of motion.
An Exact Algorithm for Kinodynamic Planning in the Plane.
An example of a non-degenerate precession possessing two distinct pairs of axes
In the present paper we provide an interesting example of a non-degenerate precession possessing two distinct pairs , of axes of precession and figure. Thus the problem arises of the existence of classes of precessions possessing a unique axis of precession and a unique axis of figure. In the fourth section we show that the class of non-degenerate regular precessions enjoys this property.