This work develops the geometry and dynamics of mechanical systems with nonholonomic
constraints and symmetry from the perspective of Lagrangian mechanics and with a view to …

One of the most important developments in exoplanet science in the past decade is the
discovery of multi-planet systems with sub-Neptune-sized planets interior to 1~ AU. This …

Symmetry has always played an important role in mechanics, from fundamental formulations
of basic principles to concrete applications. The theme of the book is to develop the basic …

Nonholonomic systems provide an important class of mechanical control systems. One
reason for this importance is that nonintegrability is essential to both the mechanics and the …

This paper gives a review of integration algorithms for finite dimensional mechanical
systems that are based on discrete variational principles. The variational technique gives a …

We study Euler–Poincaré systems (ie, the Lagrangian analogue of Lie–Poisson Hamiltonian
systems) defined on semidirect product Lie algebras. We first give a derivation of the Euler …

The use of the symmetries of a physical system in the study of its dynamics has a long
history that goes back to the founders of c1assical mechanics. Symmetry-based tech niques …

Consider a thin, flexible wire of fixed length that is held at each end by a robotic gripper. Any
curve traced by this wire when in static equilibrium is a local solution to a geometric optimal …

This booklet studies the geometry of the reduction of Lagrangian systems with symmetry in a
way that allows the reduction process to be repeated; that is, it develops a context for …

Recent works have shown that physics-inspired architectures allow the training of deep
graph neural networks (GNNs) without oversmoothing. The role of these physics is unclear …