Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque

New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of a rigid body with a spherical ellipsoid of inertia. In particular, by following Hestenes' theory, the rotational motion of an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a "virtual" spherical body with respect to the inertial frame and the motion of the axially symmetric body with respect to this "virtual" body. The kinematic solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" version of the journal paper. The following typos present in the Journal version are HERE corrected: 1) Definition of \beta, before Eq. 18; 2) sign in the statement of Theorem 3; 3) Sign in Eq. 53; 4)Item r_0 in Eq. 58; 5) Item R_{SN}(0) in Eq. 6

Chloroquine resistant vivax malaria in a pregnant woman on the western border of Thailand

Chloroquine (CQ) resistant vivax malaria is spreading. In this case, Plasmodium vivax infections during pregnancy and in the postpartum period were not satisfactorily cleared by CQ, despite adequate drug concentrations. A growth restricted infant was delivered. Poor susceptibility to CQ was confirmed in-vitro and molecular genotyping was strongly suggestive of true recrudescence of P. vivax. This is the first clinically and laboratory confirmed case of two high-grade CQ resistant vivax parasite strains from Thailand

Systems of Hess-Appel'rot type

We construct higher-dimensional generalizations of the classical Hess-Appel'rot rigid body system. We give a Lax pair with a spectral parameter leading to an algebro-geometric integration of this new class of systems, which is closely related to the integration of the Lagrange bitop performed by us recently and uses Mumford relation for theta divisors of double unramified coverings. Based on the basic properties satisfied by such a class of systems related to bi-Poisson structure, quasi-homogeneity, and conditions on the Kowalevski exponents, we suggest an axiomatic approach leading to what we call the "class of systems of Hess-Appel'rot type".Comment: 40 pages. Comm. Math. Phys. (to appear

Стратегічне планування як основний інструмент ефективності підприємства

Наук. кер.: А.Ю. Жулавськи

Evaluation of three parasite lactate dehydrogenase-based rapid diagnostic tests for the diagnosis of falciparum and vivax malaria

BACKGROUND: In areas where non-falciparum malaria is common rapid diagnostic tests (RDTs) capable of distinguishing malaria species reliably are needed. Such tests are often based on the detection of parasite lactate dehydrogenase (pLDH). METHODS: In Dawei, southern Myanmar, three pLDH based RDTs (CareStart Malaria pLDH (Pan), CareStart Malaria pLDH (Pan, Pf) and OptiMAL-IT)were evaluated in patients presenting with clinically suspected malaria. Each RDT was read independently by two readers. A subset of patients with microscopically confirmed malaria had their RDTs repeated on days 2, 7 and then weekly until negative. At the end of the study, samples of study batches were sent for heat stability testing. RESULTS: Between August and November 2007, 1004 patients aged between 1 and 93 years were enrolled in the study. Slide microscopy (the reference standard) diagnosed 213 Plasmodium vivax (Pv) monoinfections, 98 Plasmodium falciparum (Pf) mono-infections and no malaria in 650 cases. The sensitivities (sens) and specificities (spec), of the RDTs for the detection of malaria were- CareStart Malaria pLDH (Pan) test: sens 89.1% [CI95 84.2-92.6], spec 97.6% [CI95 96.5-98.4]. OptiMal-IT: Pf+/- other species detection: sens 95.2% [CI95 87.5-98.2], spec 94.7% [CI95 93.3-95.8]; non-Pf detection alone: sens 89.6% [CI95 83.6-93.6], spec 96.5% [CI95 94.8-97.7]. CareStart Malaria pLDH (Pan, Pf): Pf+/- other species: sens 93.5% [CI95 85.4-97.3], spec 97.4% [95.9-98.3]; non-Pf: sens 78.5% [CI95 71.1-84.4], spec 97.8% [CI95 96.3-98.7]. Inter-observer agreement was excellent for all tests (kappa > 0.9). The median time for the RDTs to become negative was two days for the CareStart Malaria tests and seven days for OptiMAL-IT. Tests were heat stable up to 90 days except for OptiMAL-IT (Pf specific pLDH stable to day 20 at 35 degrees C). CONCLUSION: None of the pLDH-based RDTs evaluated was able to detect non-falciparum malaria with high sensitivity, particularly at low parasitaemias. OptiMAL-IT performed best overall and would perform best in an area of high malaria prevalence among screened fever cases. However, heat stability was unacceptable and the number of steps to perform this test is a significant drawback in the field. A reliable, heat-stable, highly sensitive RDT, capable of diagnosing all Plasmodium species has yet to be identified

Introduction to non-linear mechanics

A little used parameterization of the three-dimensional rotation group is taken as basis in deriving an easily integrable kinematic relation (a 4-vector linear differential equation) for the attitude rate, in terms of the present attitude and angular velocity of one reference frame relative to another. If the angular velocity is known and• well behaved Pa ROBABLY the principal reason for difficulty in visualizing continuous rigid-body motions lies in the noncommutativity of finite rotations. This manifests itself analytically in that direct integration of the angular velocity time history does not give anything related to final attitude. In other words, the angular velocity o> when multiplied by dt does not constitute the differential of a set of coordinates which can adequately represent attitude; i.e., is not an'attitude rate. A complete solution to Euler's equations, for torques independent of attitude, is therefore inherently the sum of two separate parts. We first obtain co(<) from the dynamical equations and then employ it in usually nonlinear equations for the particular kind of attitude coordinates used. The subject matter of this paper is concerned with the latter, purely geometric aspect. A special set of coordinate variables is introduced which after much manipulation results in a linear differential equation for the attitude (a 4-vector) with its timevarying matrix constructed solely from the angular velocity (a 3-vector). An infinite series expansion in integrals is shown. There is a curious recursiveness owing to properties that the matrix exhibits upon being rewritten in a certain way. In the text will be found a free interchange between matrix and dyadic terminology but. this should cause no confusion. Transformation of a Vector Imagine a certain reference frame in which a straight wire of circular cross section (with one end at the origin) is represented 1 This is the first in a proposed series of papers dealing with rotation kinematics. Discussion of this paper should be addressed to the Editorial Department, ASME, United Engineering Center, 345 East 47th Street, New York, N. Y. 10017, and will be accepted until July 10, 1964. Discussion received after the closing date will be returned. Manuscript received by ASME Applied Mechanics Division, April 29, 1963. Paper No. 63-WA-60