A derivation of the Jacobi identity in classical mechanics.
Jacobi identity in classical mechanics
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Jacobi identity in classical mechanics
Identity between growth hormone degrading activity of pituitary gland and plasmin
Matrix identity associated with linear digital filtering and recursive estimating determined using matrix projection operators and properties
Design description and performance test results from identical Brayton heat exchange units
Direct near identity canonical transformations
Capacity calculation of N identical discrete memoryless nonsingular channels cascade, discussing dependence on eigenvalues and eigenvectors of subchannel transition matrices
Performance tests of two identical Brayton cycle heat exchanger units consisting of recuperator, heat sink exchanger and ducting in combination with turbine
Hot performance tests of three identical Brayton rotating units on gas bearings
A collimator is disclosed for examining the spatial location of distant sources of radiation and for imaging by projection, small, near sources of radiation. The collimator consists of a plurality of plates, all of which are pierced with an identical random array of apertures. The plates are mounted perpendicular to a common axis, with like apertures on consecutive plates axially aligned so as to form radiation channels parallel to the common axis. For near sources, the collimator is interposed between the source and a radiation detector and is translated perpendicular to the common axis so as to project radiation traveling parallel to the common axis incident to the detector. For far sources the collimator is scanned by rotating it in elevation and azimuth with a detector to determine the angular distribution of the radiation from the source.
The specific results reported refer to head-on collisions between identical polytropes of index 3 having solar mass and radius. If the polytropes were initially at rest at infinity, then about 5% of the combined mass is lost by ejection following collision. The volatilized mass fraction rises to about 18% for an initial relative collision velocity of 1000 km/sec at infinite separation, and to about 60% for the 2000 km/sec case. Since the initial kinetic and gravitational energies balance for a relative velocity of 1512 km/sec at infinity, it may be seen that net coalescence persists to velocities somewhat in excess of this figure. Mass ejection takes place in two ways simultaneously: (1) by a rapid sideward expulsion of fluid in a massive lateral sheet normal to the collision axis, and (2) as a result of two recoil shocks which lead momentum flows backward along this axis. The lateral effect has similarities to the expansion of gas into a vacuum i.e., shocks are not involved. However, the ejection of material from the rear colliding hemisphere due to the recoil shocks predominates at low collision velocities. As the velocity increases, both effects strengthen, but the lateral expulsion intensifies more rapidly than the recoil shocks.
The robustness of reliability predictions based on the exponential failure law is investigated under possible deviations within the Weibull family of failure distributions. Regions of robustness are provided for series systems of N identical components, N = 1(1)15; i.e., regions in the space of the Weibull shape parameter, within which one may safely use the exponential prediction procedure and have no more than a prespecified error.
Four subjects compared successively presented pairs of line patterns for a match between any lines in the pattern (similarity) and for a match between all lines (identity). The encoding or study times for pattern recognition from immediate memory and the latency in responses to comparison stimuli were examined. Qualitative differences within and between subjects were most evident in study times.
An example is provided of two convolutional codes that have the same transmission gain but whose dual codes do not. This shows that no analog of the MacWilliams identity for block codes can exist relating the transmission gains of a convolutional code and its dual.
Four identical four place, high wing, single engine airplane specimens with nominal masses of 1043 kg were crash tested at the Langley Impact Dynamics Research Facility under controlled free flight conditions. These tests were conducted with nominal velocities of 25 m/sec along the flight path angles, ground contact pitch angles, and roll angles. Three of the airplane specimens were crashed on a concrete surface; one was crashed on soil. Crash tests revealed that on a hard landing, the main landing gear absorbed about twice the energy for which the gear was designed but sprang back, tending to tip the airplane up to its nose. On concrete surfaces, the airplane impacted and remained in the impact attitude. On soil, the airplane flipped over on its back. The crash impact on the nose of the airplane, whether on soil or concrete, caused massive structural crushing of the forward fuselage. The liveable volume was maintained in both the hard landing and the nose down specimens but was not maintained in the roll impact and nose down on soil specimens.
It is a standard procedure to analyze a flexible vehicle in terms of its vibration frequencies and mode shapes. However, the entire mode shape is not needed per se, but two integrals of the mode shape, pi and hi, which correspond to the momentum and angular momentum in Mode i. Together with the natural frequencies omega-i, these modal parameters satisfy several important identities, 25 of which are derived in this paper. Expansions in terms of both constrained and unconstrained modes are considered. A simple illustrative example is included. The paper concludes with some remarks on the theoretical and practical utility of these results, and several potential extensions to the theory are suggested.
In an attempt to gain some insight into the problem of how close particles have to be on the average before phase effects become important, the cross section and phase matrices for two identical particles as a function of the distance between their centers for both broadside and end-on illumination have been calculated. The point dipole approximation is employed to build two pseudospherical particles each consisting of 32 dipoles with an effective size parameter of 0.9283 and refractive index of 1.54-0.0i. In regard to cross sections, it is found that in certain cases several percent deviation from the converged value, which is twice the single particle cross section, could be found up to distances of separation of 25 single particle diameters. The maxima and minima in the cross section curves can be explained in terms of simple interference effects. Also the element P11 of the phase matrix showed a great deal of structure, and the position of maxima and minima could be explained by phase shift analysis.
Three identical four place, low wing single engine airplane specimens with nominal masses of 1043 kg were crash tested under controlled free flight conditions. The tests were conducted at the same nominal velocity of 25 m/sec along the flight path. Two airplanes were crashed on a concrete surface (at 10 and 30 deg pitch angles), and one was crashed on soil (at a -30 deg pitch angle). The three tests revealed that the specimen in the -30 deg test on soil sustained massive structural damage in the engine compartment and fire wall. Also, the highest longitudinal cabin floor accelerations occurred in this test. Severe damage, but of lesser magnitude, occurred in the -30 deg test on concrete. The highest normal cabin floor accelerations occurred in this test. The least structural damage and lowest accelerations occurred in the 10 deg test on concrete.
A small but interesting class of optimal control problems featuring a scalar control appearing linearly is equivalent to the class of identically nonregular problems in the Calculus of Variations. It is shown that a condition due to Mancill (1950) is equivalent to the generalized Legendre-Clebsch condition for this narrow class of problems.