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The car with $N$ trailers : characterisation of the singular configurations

Frédéric Jean (1996)

ESAIM: Control, Optimisation and Calculus of Variations

The car with N Trailers : characterization of the singular configurations

Frédéric Jean (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study the problem of the car with N trailers. It was proved in previous works ([9], [12]) that when each trailer is perpendicular with the previous one the degree of nonholonomy is Fn+3 (the (n+3)-th term of the Fibonacci's sequence) and that when no two consecutive trailers are perpendicular this degree is n+2. We compute here by induction the degree of non holonomy in every state and obtain a partition of the singular set by this degree of non-holonomy. We give also for...

The Drazin inverse in multibody system dynamics.

P. Rentrop, C. Führer, B. Simeon (1993)

Numerische Mathematik

The Foldy-Wouthuysen transformation in the two-particle case

H. Sazdjian (1987)

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

The geometry and mechanics of multi-particle systems

Toshihiro Iwai, Akitomo Tachibana (1999)

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

The Invariance of Poincaré's Generating Function for Canonical Transformations.

Alan Weinstein (1972)

Inventiones mathematicae

The inverse problem for flat kinetic minus potencial Lagrangians.

G. Thompson, G. E. Prince (2001)

Extracta Mathematicae

The $n$ -centre problem of celestial mechanics for large energies

Andreas Knauf (2002)

Journal of the European Mathematical Society

We consider the classical three-dimensional motion in a potential which is the sum of $n$ attracting or repelling Coulombic potentials. Assuming a non-collinear configuration of the $n$ centres, we find a universal behaviour for all energies $E$ above a positive threshold. Whereas for $n = 1$ there are no bounded orbits, and for $n = 2$ there is just one closed orbit, for $n \geq 3$ the bounded orbits form a Cantor set. We analyze the symbolic dynamics and estimate Hausdorff dimension and topological entropy of this hyperbolic set....