107,891 research outputs found
H. L. Biggs, and Cato Hightower
No full textH. L. Biggs, left, new policeman who was sworn with 10 other rookies, gets congratulations from the Police Chief Cato Hightower.https://mavmatrix.uta.edu/specialcollections_startelegram1950s/28274/thumbnail.jp
Ernie Biggs Athletic Training Facility
No full textEntry created by John H. Herrick January 15, 1974John H. Herrick Archives: Documenting Structures at The Ohio State UniversityThe University Archives has determined that this item is of continuing value to OSU's history.Ernie Biggs Athletic Training Facility is located at 2490 Fyffe Road. Officially named "Ernie Biggs Athletic Training Facility" by Board of Trustees on November 5, 1971. Alternate names include: "Athletic Facility North" and "North Athletic Facility". The Board of Trustees on December 4,1987, named the entire complex, "The Woody Hayes Athletic Center.
Optimal path planning for nonholonomic robotics systems via parametric optimisation
No full textAbstract. Motivated by the path planning problem for robotic systems this paper considers nonholonomic path planning on the Euclidean group of motions SE(n) which describes a rigid bodies path in n-dimensional Euclidean space. The problem is formulated as a constrained optimal kinematic control problem where the cost function to be minimised is a quadratic function of translational and angular velocity inputs. An application of the Maximum Principle of optimal control leads to a set of Hamiltonian vector field that define the necessary conditions for optimality and consequently the optimal velocity history of the trajectory. It is illustrated that the systems are always integrable when n = 2 and in some cases when n = 3. However, if they are not integrable in the most general form of the cost function they can be rendered integrable by considering special cases. This implies that it is possible to reduce the kinematic system to a class of curves defined analytically. If the optimal motions can be expressed analytically in closed form then the path planning problem is reduced to one of parameter optimisation where the parameters are optimised to match prescribed boundary conditions.This reduction procedure is illustrated for a simple wheeled robot with a sliding constraint and a conventional slender underwater vehicle whose velocity in the lateral directions are constrained due to viscous damping
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Integrable quadratic Hamiltonians on the Euclidean group of motions
No full textIn this paper, we discuss the problem of globally computing sub-Riemannian curves on the Euclidean group of motions SE(3). In particular, we derive a global result for special sub-Riemannian curves whose Hamiltonian satisfies a particular condition. In this paper, sub-Riemannian curves are defined in the context of a constrained optimal control problem. The maximum principle is then applied to this problem to yield an appropriate left-invariant quadratic Hamiltonian. A number of integrable quadratic Hamiltonians are identified. We then proceed to derive convenient expressions for sub-Riemannian curves in SE(3) that correspond to particular extremal curves. These equations are then used to compute sub-Riemannian curves that could potentially be used for motion planning of underwater vehicles
Nonlinearly stable equilibria in the Sun-Jupiter-Trojan-Spacecraft four body problem
No full textThe Trojan asteroids have been highlighted as a main target for future discovery missions, which will enable key questions about the formation of our Solar system to be answered. Programs like the Japanese Jupiter and Trojan Asteroids Exploration Programme are already testing technology demonstrators like the IKAROS spacecraft to enable future interplanetary missions to Jupiter and the Trojans. In this paper an analytic analysis of the stability of the Low thrust Sun Jupiter Asteroid Spacecraft system, is presented, from a Hamiltonian point of view. Setting the three primaries in the stable Lagrangian equilateral triangle configuration, eight natural (i.e. with zero thrust) equilibrium points are identified, four of which are close to the asteroid, two stable and two unstable, when considering as primaries the Sun and any other two bodies of the Solar System. Artificial equilibria, which can be seen as low thrust perturbations of the natural ones, are then taken into account with the aim of identifying their linearly stable subset. The Lyapunov stability of these marginally stable points is then analysed using basic KAM (Kolmogorov Arnold Moser) theory and Arnold’s stability theorem. In order to apply such theorem an iterative procedure to reduce the Hamiltonian into Birkhoff’s Normal Form is applied up to fourth order, explicitly defining, at each step, the generating function of a symplectic transformation. Despite the complexity of this process, Normal Forms are a fundamental, necessary step for any application of KAM theory; such theory, transforming a non-integrable system into a sum of perturbed integrable ones, enables the computation of a high order analytical approximation of the system dynamics, plus an estimation of the discrepancy from the initial model. As an application of KAM theory, a proof of the nonlinear stability for the low thrust generated equilibrium points under non resonant conditions is found using Arnold’s stability theorem. Results show that Lyapunov stability is guaranteed along the linearly stable domain with the exception of a set of points with zero measure where the conditions to apply Arnold‘s theorem are not satisfied
Numerical modelling of mud volcanoes and their flows using constraints from the Gulf of Cadiz
No full textIt is estimated that the total number of submarine mud volcanoes is between 1000 and 100 000. Because many are associated with greenhouse gases, such as methane, it is argued that the global flux of these gases to the atmosphere from the world’s terrestrial and submarine mud volcanoes is highly significant. Clues to the processes forming submarine mud volcanoes can be found in variations to their height, shape, surface morphology, physical properties and internal structure. A model of isostatic compensation between the mud column and the sediment overlying the mud source is used to predict a depth to the mud reservoir beneath mud volcanoes. Once erupted, the general behaviour of an individual mud flow can be described and predicted using a viscous gravity-current model. The model shows that conical-shaped mud volcanoes comprise multiple, superimposed radial flows in which the thickness, eruption rate and speed of individual mud flows strongly depends on the viscosity, density and over-pressure of the erupted mud. Using these parameters, the model predicts the lowermost flows will be the oldest, thickest and have the greatest length of run-out while the uppermost flows will be the youngest, thinnest and shortest. This model is in contrast to more traditional models of stratiform mud volcano construction in which younger flows progressively bury older ones and travel furthest from the summit. Applying the model to the two mud volcanoes studied in the Gulf of Cadiz, quantitative estimates are derived for the depths to mud sources, exit and flow velocities, eruption duration and volume fluxes, flow thickness and conduit radii. For example, with an average kinematic viscosity of 1.5 m2 s?1 for the erupted mud, a density of 1.8×103 kg m?3 and a thickness for the youngest flows of about 0.5 m, the model predicts a lowermost flow thickness of 3.6 m, an average eruption duration of 7 h and a conduit radius of about 9 m. To construct a conical-shaped mud volcano of 260 m height, similar to those studied in the Gulf of Cadiz, is estimated to require a mud source at 4.6 km depth and a total of at least 100 individually erupted flows
Business Papers (MS 80-0003)
No full textLetter from J. H. Biggs of the American Indemnity Company to Joseph Seinsheimer enclosing deeds for land in Grimes County and in Houston
Singularities of optimal attitude motions
No full textThis paper considers the problem of planning optimal attitude motions for spacecraft. The extremal solutions that result from this optimization problem are characterized and their singularities identified. Following this these singularities are solved analytically inferring the form of particular optimal velocities. These particular solutions are then integrated and their corresponding motions derived independently of a local coordinate chart. These motions have the potential to be used as smooth, optimal reference trajectories for performing certain re-orientations for spacecraft
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Singularities of optimal control problems on some 6-D lie groups
No full textThis paper considers the motion planning problem for oriented vehicles travelling at unit speed in a 3-D space. A Lie group formulation arises naturally and the vehicles are modeled as kinematic control systems with drift defined on the orthonormal frame bundles of particular Riemannian manifolds, specifically, the 3-D space forms Euclidean space E-3, the sphere S-3, and the hyperboloid H'. The corresponding frame bundles are equal to the Euclidean group of motions SE(3), the rotation group SO(4), and the Lorentz group SO (1, 3). The maximum principle of optimal control shifts the emphasis for these systems to the associated Hamiltonian formalism. For an integrable case, the extremal curves are explicitly expressed in terms of elliptic functions. In this paper, a study at the singularities of the extremal curves are given, which correspond to critical points of these elliptic functions. The extremal curves are characterized as the intersections of invariant surfaces and are illustrated graphically at the singular points. It. is then shown that the projections, of the extremals onto the base space, called elastica, at these singular points, are curves of constant curvature and torsion, which in turn implies that the oriented vehicles trace helices
Low thrust propulsion in a coplanar circular restricted four body problem
No full textThis paper formulates a circular restricted four body problem (CRFBP), where the three primaries are set in the stable Lagrangian equilateral triangle configuration and the fourth body is massless. The analysis of this autonomous coplanar CRFBP is undertaken, which identies eight natural equilibria; four of which are close to the smaller body, two stable and two unstable, when considering the primaries to be the Sun and two smaller bodies of the solar system. Following this, the model incorporates `near term' low-thrust propulsion capabilities to generate surfaces of articial equilibrium points close to the smaller primary, both in and out of the plane containing the celestial bodies. A stability analysis of these points is carried out and a stable subset of them is identied. Throughout the analysis the Sun-Jupiter-Asteroid-Spacecraft system is used, for conceivable masses of a hypothetical asteroid set at the libration point L4. It is shown that eight bounded orbits exist, which can be maintained with a constant thrust less than 1:5 10􀀀4N for a 1000kg spacecraft. This illustrates that, by exploiting low-thrust technologies, it would be possible to maintain an observation point more than 66% closer to the asteroid than that of a stable natural equilibrium point. The analysis then focusses on a major Jupiter Trojan: the 624-Hektor asteroid. The thrust required to enable close asteroid observation is determined in the simplied CRFBP model. Finally, a numerical simulation of the real Sun-Jupiter-624 Hektor-Spacecraft is undertaken, which tests the validity of the stability analysis of the simplied model
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