Symmetry as a sufficient condition for a finite flex

We show that if the joints of a bar and joint framework $(G,p)$ are positioned as `generically' as possible subject to given symmetry constraints and $(G,p)$ possesses a `fully-symmetric' infinitesimal flex (i.e., the velocity vectors of the infinitesimal flex remain unaltered under all symmetry operations of $(G,p)$), then $(G,p)$ also possesses a finite flex which preserves the symmetry of $(G,p)$ throughout the path. This and other related results are obtained by symmetrizing techniques described by L. Asimov and B. Roth in their paper `The Rigidity Of Graphs' from 1978 and by using the fact that the rigidity matrix of a symmetric framework can be transformed into a block-diagonalized form by means of group representation theory. The finite flexes that can be detected with these symmetry-based methods can in general not be found with the analogous non-symmetric methods.Comment: 26 pages, 10 figure

Robotic control of the seven-degree-of-freedom NASA laboratory telerobotic manipulator

A computationally efficient robotic control scheme for the NASA Laboratory Telerobotic Manipulator (LTM) is presented. This scheme utilizes the redundancy of the seven-degree-of-freedom LTM to avoid joint limits and singularities. An analysis to determine singular configurations is presented. Performance criteria are determined based on the joint limits and singularity analysis. The control scheme is developed in the framework of resolved rate control using the gradient projection method, and it does not require the generalized inverse of the Jacobian. An efficient formulation for determining the joint velocities of the LTM is obtained. This control scheme is well suited for real-time implementation, which is essential if the end-effector trajectory is continuously modified based on sensory feedback. Implementation of this scheme on a Motorola 68020 VME bus-based controller of the LTM is in progress. Simulation results demonstrating the redundancy utilization in the robotic mode are presented

A nonlocal connection between certain linear and nonlinear ordinary differential equations/oscillators

We explore a nonlocal connection between certain linear and nonlinear ordinary differential equations (ODEs), representing physically important oscillator systems, and identify a class of integrable nonlinear ODEs of any order. We also devise a method to derive explicit general solutions of the nonlinear ODEs. Interestingly, many well known integrable models can be accommodated into our scheme and our procedure thereby provides further understanding of these models.Comment: 12 pages. J. Phys. A: Math. Gen. 39 (2006) in pres

Polarizations and differential calculus in affine spaces

Within the framework of mappings between affine spaces, the notion of $n$-th polarization of a function will lead to an intrinsic characterization of polynomial functions. We prove that the characteristic features of derivations, such as linearity, iterability, Leibniz and chain rules, are shared -- at the finite level -- by the polarization operators. We give these results by means of explicit general formulae, which are valid at any order $n$, and are based on combinatorial identities. The infinitesimal limits of the $n$-th polarizations of a function will yield its $n$-th derivatives (without resorting to the usual recursive definition), and the above mentioned properties will be recovered directly in the limit. Polynomial functions will allow us to produce a coordinate free version of Taylor's formula

Modeling the geometry of the endoplasmic reticulum network

Conference ProceedingFirst International Conference, AlCoB 2014, held in July 2014 in Tarragona, Spain.We have studied the network geometry of the endoplasmic reticulum by means of graph theoretical and integer programming models. The purpose is to represent this structure as close as possible by a class of finite, undirected and connected graphs the nodes of which have to be either of degree three or at most of degree three. We determine plane graphs of minimal total edge length satisfying degree and angle constraints, and we show that the optimal graphs are close to the ER network geometry. Basically, two procedures are formulated to solve the optimization problem: a binary linear program, that iteratively constructs an optimal solution, and a linear program, that iteratively exploits additional cutting planes from different families to accelerate the solution process. All formulations have been implemented and tested on a series of real-life and randomly generated cases. The cutting plane approach turns out to be particularly efficient for the real-life testcases, since it outperforms the pure integer programming approach by a factor of at least 10. © 2014 Springer International Publishing

Entry Guidance for the 2011 Mars Science Laboratory Mission

The 2011 Mars Science Laboratory will be the first Mars mission to attempt a guided entry to safely deliver the rover to a touchdown ellipse of 25 km x 20 km. The Entry Terminal Point Controller guidance algorithm is derived from the final phase Apollo Command Module guidance and, like Apollo, modulates the bank angle to control the range flown. For application to Mars landers which must make use of the tenuous Martian atmosphere, it is critical to balance the lift of the vehicle to minimize the range error while still ensuring a safe deploy altitude. An overview of the process to generate optimized guidance settings is presented, discussing improvements made over the last nine years. Key dispersions driving deploy ellipse and altitude performance are identified. Performance sensitivities including attitude initialization error and the velocity of transition from range control to heading alignment are presented

Euler configurations and quasi-polynomial systems

In the Newtonian 3-body problem, for any choice of the three masses, there are exactly three Euler configurations (also known as the three Euler points). In Helmholtz' problem of 3 point vortices in the plane, there are at most three collinear relative equilibria. The "at most three" part is common to both statements, but the respective arguments for it are usually so different that one could think of a casual coincidence. By proving a statement on a quasi-polynomial system, we show that the "at most three" holds in a general context which includes both cases. We indicate some hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial framework.Comment: 21 pages, 6 figure

Viking navigation

A comprehensive description of the navigation of the Viking spacecraft throughout their flight from Earth launch to Mars landing is given. The flight path design, actual inflight control, and postflight reconstruction are discussed in detail. The preflight analyses upon which the operational strategies and performance predictions were based are discussed. The inflight results are then discussed and compared with the preflight predictions and, finally, the results of any postflight analyses are presented

On Two Complementary Types of Total Time Derivative in Classical Field Theories and Maxwell's Equations

Close insight into mathematical and conceptual structure of classical field theories shows serious inconsistencies in their common basis. In other words, we claim in this work to have come across two severe mathematical blunders in the very foundations of theoretical hydrodynamics. One of the defects concerns the traditional treatment of time derivatives in Eulerian hydrodynamic description. The other one resides in the conventional demonstration of the so-called Convection Theorem. Both approaches are thought to be necessary for cross-verification of the standard differential form of continuity equation. Any revision of these fundamental results might have important implications for all classical field theories. Rigorous reconsideration of time derivatives in Eulerian description shows that it evokes Minkowski metric for any flow field domain without any previous postulation. Mathematical approach is developed within the framework of congruences for general 4-dimensional differentiable manifold and the final result is formulated in form of a theorem. A modified version of the Convection Theorem provides a necessary cross-verification for a reconsidered differential form of continuity equation. Although the approach is developed for one-component (scalar) flow field, it can be easily generalized to any tensor field. Some possible implications for classical electrodynamics are also explored.Comment: no figure

Long-term exposure to outdoor air pollution and the incidence of chronic obstructive pulmonary disease in a national English cohort.

OBJECTIVES: The role of outdoor air pollution in the incidence of chronic obstructive pulmonary disease (COPD) remains unclear. We investigated this question using a large, nationally representative cohort based on primary care records linked to hospital admissions. METHODS: A cohort of 812 063 patients aged 40-89 years registered with 205 English general practices in 2002 without a COPD diagnosis was followed from 2003 to 2007. First COPD diagnoses recorded either by a general practitioner (GP) or on admission to hospital were identified. Annual average concentrations in 2002 for particulate matter with an aerodynamic diameter <10 µm (PM10) and <2.5 µm (PM2.5), nitrogen dioxide (NO2), ozone and sulfur dioxide (SO2) at 1 km(2) resolution were estimated from emission-based dispersion models. Hazard ratios (HRs) per interquartile range change were estimated from Cox models adjusting for age, sex, smoking, body mass index and area-level deprivation. RESULTS: 16 034 participants (1.92%) received a COPD diagnosis from their GP and 2910 participants (0.35%) were admitted to hospital for COPD. After adjustment, HRs for GP recorded COPD and PM10, PM2.5 and NO2 were close to unity, positive for SO2 (HR=1.07 (95% CI 1.03 to 1.11) per 2.2 µg/m(3)) and negative for ozone (HR=0.94 (0.89 to 1.00) per 3 µg/m(3)). For admissions HRs for PM2.5 and NO2 remained positive (HRs=1.05 (0.98 to 1.13) and 1.06 (0.98 to 1.15) per 1.9 µg/m(3) and 10.7 µg/m(3), respectively). CONCLUSIONS: This large population-based cohort study found limited, inconclusive evidence for associations between air pollution and COPD incidence. Further work, utilising improved estimates of air pollution over time and enhanced socioeconomic indicators, is required to clarify the association between air pollution and COPD incidence