The International Symposium on Nuclear Structure Physics (NP2001) was
held in Gottingen Germany, March 5-8, 2001. The aim of the Symposium
was to discuss recent achievements and new initiatives for research in nuclear
structure and to celebrate the career of Peter von Brentano.
The Series ‘Topics in Molecular Organization and Engineering’ was initiated by
the Symposium ‘Molecules in Physics, Chemistry, and Biology’, which was held
in Paris in 1986. Appropriately dedicated to Professor Raymond Daudel, the
symposium was both broad in its scope and penetrating in its detail. The sections
of the symposium were: 1. The Concept of a Molecule; 2. Statics and Dynamics
of Isolated Molecules; 3. Molecular Interactions, Aggregates and Materials; 4.
Molecules in the Biological Sciences, and 5. Molecules in Neurobiology and So-
This work develops the geometry and dynamics of mechanical systems with
nonholonomic constraints and symmetry from the perspective of Lagrangian me-
chanics and with a view to control-theoretical applications. The basic methodology
is that of geometric mechanics applied to the Lagrange-d’Alembert formulation,
generalizing the use of connections and momentum maps associated with a given
symmetry group to this case.
Few of us can any longer keep up with the flood of scientific literature, even
in specialized subfields. Any attempt to do more and be broadly educated
with respect to a large domain of science has the appearance of tilting at
windmills. Yet the synthesis of ideas drawn from different subjects into new,
powerful, general concepts is as valuable as ever, and the desire to remain
educated persists in all scientists.
Motor vehicles, like most machines, have a general bilateral symmetry. Only hypotheses can be advanced to explain why this occurs. Certainly to have a symmetry plane simpliﬁes the study of the dynamic behavior of the system, for it can be modelled, within certain limits, using uncoupled equations. However, the reason is likely to be above all an aesthetic one: symmetry is considered an essential feature in most deﬁnitions of beauty.
A speciﬁc example in which the theory developed here is quite crucial is
the analysis of locomotion for the snakeboard, which we study in some detail
in Section 8.4. The snakeboard is a modiﬁed version of a skateboard in which
locomotion is achieved by using a coupling of the nonholonomic constraints with
the symmetry properties of the system. For that system, traditional analysis of
the complete dynamics of the system does not readily explain the mechanism of
A related modern example is the snakeboard (see LEWIS,OSTROWSKI,MURRAY
&BURDICK ),which shares some of the features of these examples butwhich
has a crucial difference as well. This example, likemany of the others, has the sym-
metry group SE(2) of Euclidean motions of the plane but, now, the corresponding
momentum is not conserved. However, the equation satisﬁed by the momentum
associated with the symmetry is useful for understanding the dynamics of the prob-
lem and how group motion can be generated.
Problems of nonholonomic mechanics, including many problems in robotics,
wheeled vehicular dynamics and motion generation, have attracted considerable
attention. These problems are intimately connected with important engineering
issues such as path planning, dynamic stability, and control.Thus, the investigation
of many basic issues, and in particular, the role of symmetry in such problems,
remains an important subject today.