Page 1 Next

## Displaying 1 – 20 of 246

Showing per page

### A BF-regularization of a nonstationary two-body problem under the Maneff perturbing potential.

Extracta Mathematicae

The process of transforming singular differential equations into regular ones is known as regularization. We are specially concerned with the treatment of certain systems of differential equations arising in Analytical Dynamics, in such a way that, accordingly, the regularized equations of motion will be free of singularities.

### A. C. Clarke's Space Odyssey and Newton's law of gravity

Programs and Algorithms of Numerical Mathematics

In his famous tetralogy, Space Odyssey, A. C. Clarke called the calculation of a motion of a mass point in the gravitational field of the massive cuboid a classical problem of gravitational mechanics. This article presents a proposal for a solution to this problem in terms of Newton's theory of gravity. First we discuss and generalize Newton's law of gravitation. We then compare the gravitational field created by the cuboid -- monolith, with the gravitational field of the homogeneous sphere. This...

### A continuation method for motion-planning problems

ESAIM: Control, Optimisation and Calculus of Variations

We apply the well-known homotopy continuation method to address the motion planning problem (MPP) for smooth driftless control-affine systems. The homotopy continuation method is a Newton-type procedure to effectively determine functions only defined implicitly. That approach requires first to characterize the singularities of a surjective map and next to prove global existence for the solution of an ordinary differential equation, the Wazewski equation. In the context of the MPP, the aforementioned...

### A continuation method for motion-planning problems

ESAIM: Control, Optimisation and Calculus of Variations

We apply the well-known homotopy continuation method to address the motion planning problem (MPP) for smooth driftless control-affine systems. The homotopy continuation method is a Newton-type procedure to effectively determine functions only defined implicitly. That approach requires first to characterize the singularities of a surjective map and next to prove global existence for the solution of an ordinary differential equation, the Wazewski equation. In the context of the MPP, the aforementioned...

### A discrete contact model for crowd motion

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: we first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people. The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here the...

### A discrete contact model for crowd motion

ESAIM: Mathematical Modelling and Numerical Analysis

The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: we first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people. The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here...

### A discretization of the nonholonomic Chaplygin sphere problem.

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

### A first-order canonical set of generalized Jacobi-type variables for hyperbolic orbital motion.

Extracta Mathematicae

### A generalized theory of classical mechanics for the two body problem

Rendiconti del Seminario Matematico della Università di Padova

### A geometric setting for classical molecular dynamics

Annales de l'I.H.P. Physique théorique

### A geometric study of many-body systems.

Lobachevskii Journal of Mathematics

### A group theoretic approach to generalized harmonic vibrations in a one dimensional lattice.

International Journal of Mathematics and Mathematical Sciences

### À l'infini en temps fini

Séminaire Bourbaki

### A methodology for the numerical computation of normal forms, centre manifolds and first integrals of Hamiltonian systems.

Experimental Mathematics

### A new look at classical mechanics of constrained systems

Annales de l'I.H.P. Physique théorique

### A proof of universality of arc length as time parameter in Kepler problems.

Extracta Mathematicae

Annales de l'I.H.P. Physique théorique

### A remarkable periodic solution of the three-body problem in the case of equal masses.

Annals of Mathematics. Second Series

### A sequence adapted from the movement of the center of mass of two planets in solar system

Communications in Mathematics

In this paper we derive a sequence from a movement of center of~mass of arbitrary two planets in some solar system, where the planets circle on concentric circles in a same plane. A trajectory of center of mass of the planets is discussed. A sequence of points on the trajectory is chosen. Distances of the points to the origin are calculated and a distribution function of a sequence of the distances is found.

### A singular lagrangian model for N-body relativistic interactions

Annales de l'I.H.P. Physique théorique

Page 1 Next