Nilpotent Bases for a Class of Non-Integrable Distributions with Applications to Trajectory Generation for Nonholonomic Systems

This paper develops a constructive method for finding a nilpotent basis for a special class of smooth nonholonomic distributions. The main tool is the use of the Goursat normal form theorem which arises in the study of exterior differential systems. The results are applied to the problem of finding a set of nilpotent input vector fields for a nonholonomic control system, which can then used to construct explicit trajectories to drive the system between any two points. A kinematic model of a rolling penny is used to illustrate this approach. The methods presented here extend previous work using "chained form" and cast that work into a coordinate-free setting

Unstitching Scarlet Letters?: Prosecutorial Discretion and Expungement

This Article argues that scholarly discussions about prosecutorial discretion need to extend their focus beyond the exercise of prosecutorial judgment pretrial or questions of factual and legal guilt. Given that the primary role of the prosecutoris to do “justice,” this Article calls for increased attention to the exercise of discretion after the guilt phase is complete, specifically in the context of expungement of nonconviction andconviction information. It offers a framework for exercising such discretion and, in doing so, hopes to initiate additional conversation about the role of prosecutors during the phases that follow arrest and prosecution

Children and Schooling in New South Wales, 1860-1920

In the second half of the nineteenth century in New South Wales the introduction and spread of mass schooling added a significant workload to the lives of most children. The ideal of modern schooling placed children in a classroom, morning and afternoon, five days a week, for most weeks of the year. In effect the schoolroom became a kind of workplace, albeit unpaid. Schoolwork became a given for nearly all children, whatever their household's societal position. Socio-economic status, race and gender affected and mediated a child's experience of schooling, but they did not remove children from the school experience. The school system functioned to reproduce and impart values considered important by the respectable and powerful in society. The mass schooling program established remains in place today. Consolidated and extended, it nevertheless retains and continues many original values and functions, and still prescribes experience and containment for children.children, schooling, New South Wales

The Origin of Chaos in the Outer Solar System

Classical analytic theories of the solar system indicate that it is stable, but numerical integrations suggest that it is chaotic. This disagreement is resolved by a new analytic theory. The theory shows that the chaos among the Jovian planets results from the overlap of the components of a mean motion resonance among Jupiter, Saturn, and Uranus, and provides rough estimates of the Lyapunov time (10 million years) and the dynamical lifetime of Uranus (10^{18} years). The Jovian planets must have entered the resonance after all the gas and most of the planetesimals in the protoplanetary disk were removed.Comment: 19 pages, 3 figures, to appear in Scienc

Working Boarders: The Boarding Out Scheme in New South Wales, 1820-1920

boarding out scheme, New South Wales