Variational integrators and time-dependent lagrangian systems

This paper presents a method to construct variational integrators for time-dependent lagrangian systems. The resulting algorithms are symplectic, preserve the momentum map associated with a Lie group of symmetries and also describe the energy variation.Comment: 8 page

Towards a Hamilton-Jacobi Theory for Nonholonomic Mechanical Systems

In this paper we obtain a Hamilton-Jacobi theory for nonholonomic mechanical systems. The results are applied to a large class of nonholonomic mechanical systems, the so-called \v{C}aplygin systems.Comment: 13 pages, added references, fixed typos, comparison with previous approaches and some explanations added. To appear in J. Phys.

Tulczyjew's triples and lagrangian submanifolds in classical field theories

In this paper the notion of Tulczyjew's triples in classical mechanics is extended to classical field theories, using the so-called multisymplectic formalism, and a convenient notion of lagrangian submanifold in multisymplectic geometry. Accordingly, the dynamical equations are interpreted as the local equations defining these lagrangian submanifolds.Comment: 29 page

Discrete variational integrators and optimal control theory

A geometric derivation of numerical integrators for optimal control problems is proposed. It is based in the classical technique of generating functions adapted to the special features of optimal control problems.Comment: 17 page

Some applications of semi-discrete variational integrators to classical field theories

We develop a semi-discrete version of discrete variational mechanics with applications to numerical integration of classical field theories. The geometric preservation properties are studied.Comment: 14 page

Geometric numerical integration of nonholonomic systems and optimal control problems

A geometric derivation of numerical integrators for nonholonomic systems and optimal control problems is obtained. It is based in the classical technique of generating functions adapted to the special features of nonholonomic systems and optimal control problems.Comment: 6 pages, 1 figure. Submitted to IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Sevilla 200

A new geometric setting for classical field theories

A new geometrical setting for classical field theories is introduced. This description is strongly inspired in the one due to Skinner and Rusk for singular lagrangians systems. For a singular field theory a constraint algorithm is developed that gives a final constraint submanifold where a well-defined dynamics exists. The main advantage of this algorithm is that the second order condition is automatically included.Comment: 22 page

The natural and capital infrastructure of potential post-electrification wealth creation in Kenya

Background It is widely accepted that electricity is an important element for improving levels of human development and wealth creation in rural areas. Yet, little research has explored the conditions under which electrification could lead to wealth creation post-electrification. Using Kenya as a case study, this paper uses natural capital (NC) and infrastructural capital (IC) data to compare the enabling environments under which electrification could lead to wealth creation (and persistent demand for electricity) post-electrification. Methods We use multiple spatial data sets to create three different metrics for NC and IC and use them to create a micro-enterprise development index (MED index). NC data is composed of water body data (major rivers and access to irrigation infrastructure), soil data (soil quality and agro-ecological potential), and agricultural data (crop intensity and diversity). IC is composed of spatial data spanning major towns, first and second tier roads, electricity infrastructure (transmission grid, location of government, and entrepreneur run off-grid electrification projects), population density, access to education, trade centers (markets), healthcare, and access to financial services. We perform feature scaling on NC and IC data and use them to create a MED index, which we use to represent the potential for rural micro-enterprises to create wealth, post-electrification. We compare this spatial proxy to a nightlights GDP per capita proxy developed by the World Bank in 2015 and provide a discussion highlighting the benefits and drawbacks of our approach and of using nightlights as a single metric for wealth in rural areas. Results In Kenya, infrastructural capital follows natural capital. Regions with greater natural capital have relatively higher development and penetration of infrastructural capital. We observe a large discrepancy between our MED index and the nightlights income proxy, which could be caused by an underestimate of economic activity by nightlights, and an overestimate by the MED index, being that it is a measure of “potential” wealth (as opposed to current wealth). Conclusions A spatial aggregation of natural and infrastructural capital, and nightlights data, could be an accurate demand-side input for electrification supply-side models including grid-expansion and off-grid strategies