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A sample of forty-two chronic schizophrenics were randomly assigned to one of two groups given three sessions of either massed or spaced practice on a pursuit rotor, and a group of sixteen depressives were given massed practice only. The results suggest that there are differences between the learning curves of these groups when compared with those of normals. Notable among these differences is the absence of reminiscence after massed practice, and the failure of spaced practice to give the usual distinct superiority over massed. Statistical analysis of the data confirms the inferiority of the psychotics in respect of level of learning, but fails to show any other marked differences in the nature of the learning curves. The results are discussed primarily in the context of Hullian learning theory.

A numerical procedure for solving the rotational differential equation for the planar H + H2 reaction in natural difurcation coordinates is described. The procedure has the advantage that it may be applied uniformly over the entire range of the reaction coordinate. The symmetry of the differential equation is utilized to simplify the form of the wavefunctions, and their asymptotic behavior provides a state labeling criterion. The conditions under which any pair of energy levels may become either identically or nearly degenerate is investigated. It is shown that as the reactants approach the transition state (s=O), the rotational wavefunctions smoothly pass through forms characteristic of free rotation, hindered rotation, and finally of a bending vibration. At s=O, equal probability density is shown to be highly localized at the entrance of each rearrangement channel.

The rotational contours of the naphthalene absorption bands at 32 458 and 32 521 cm−1 are re-analyzed, in asymmetric, rigid-rotor approximation. They are confirmed to exhibit transition moments in the plane of the molecule, the first along the central carbon—carbon bond and the second along the in-plane direction perpendicular to the first; that is the bands are type-B and type-A, respectively. The parameters that are well determined are the band center and the changes of two inertial constants for type-B and the band center only for type-A.

Certain matrix elements of P n =( λP x + μP y + νP z ) n where n takes on the values one through five are calculated for a slightly asymmetric rotor molecule in a perturbation theory expansion in terms of the molecular asymmetry parameter b . The expressions are correct to second order in b for P 1 , to first order in b for P 3 and P 4 , and to zeroth order in b for P 5 . Two tables are presented from which these matrix elements can be simply transformed into any of the conventional axis representations. The results are useful for the interpretation of effects arising from perturbations, such as centrifugal distortion and internal rotation, which commonly appear in the microwave spectra of slightly-asymmetric-rotor molecules.

A theory for the internal rotation in molecules where the internal rotor is not a symmetric top has been formulated. The principal feature of the theory is the expansion of the rotational constants for the molecule in a converging series of sinnα and cosnα. This allows for the straightforward evaluation of certain integrals appearing in the development of the theory.In addition, the theory is applied specifically to CH2DCOH, CD2HCOH, and CHOOCH2D in the analysis of the microwave rotational spectra for these molecules. For CH2DCOH the height of the potential barrier hindering the internal motion is found to be V=410 cm—1, which is consistent with the barrier height for other species of acetaldehyde. To fit the spectra of CD2HCOH and CHOOCH2D a slight rotation of the effective principal axes must be made to obtain a consistent potential barrier.The results of the calculation indicate that (1) the theory is readily applicable in the determination of the barrier heights of the more general molecules, and (2) ...

The present paper, a problem in autogiro rotor stress analysis, can be outlined as follows: 1. Calculation of the characteristics of a typical autogiro employed for illustrative purposes. 2. Derivation of formulas for bending moments in the plane of flapping taking into account the effects of the weight of the blade, centrifugal force, inertia forces in flapping and aerodynamic thrust. 3. Examination of the effect of the azimuth angle ^ on bending moments at a given point on the blade. 4. Effect of variations in /*, the tip speed ratio, on the bending moment a t a given point on the blade. 5. Examination of the effect of the ratio r/R on bending moments. 6. Formulas for the centrifugal relief of bending moments. 7. Comparison of bending moments obtained by the above methods with the bending moments obtained by the use of empirical formulas available hitherto. Certain simplifications have been employed. These are: (a) Only the first harmonic of the flapping motion is considered. (b) Terms of a higher order than A* are neglected. (c) The flow through the rotor disk is considered uniform. (d) Mass distribution along the span of the blade is uniform. (e) The product EI is uniform along the span of the blade. (f) Stalling effects that may occur at portions of the blade are neglected. (g) Periodic twisting of the blade is not taken into account. The underlying aerodynamic theory is well known to those interested in the autogiro and no presentation of such theory is made in the present paper.

The problem of the design of rotor blades within the framework of the hypothesis of an infinitely large number of blades reduces to the solution of an inverse axisymmetric problem. In the Bauersfeld-Voznesenskii formulation [1–3] this problem may be stated as follows: for given meridional flow and angular rotor velocity, construct the blade surface S 2 ′ (Fig. 1) passing through a given inlet ab (or exit cd) edge and a given line of intersection ad of the blade with one axisymmetric stream surface of the given meridional flow. Henceforth, S 2 ′ will be used to designate the median (or concave) surface of the blade, which, under certain conditions, coincides with the median interblade stream surface abcd.

Introduction T method of multiblade coordinates introduced by Coleman is a powerful technique for describing the motion of a multibladed helicopter rotor. Multiblade coordinates describe the overall rotor motion in a nonrotating coordinate frame fixed in the helicopter body. This provides advantages over individual blade coordinates which describe the motion of the individual blades in a frame rotating with the rotor. Some advantages are 1) the overall rotor motion, which includes the motion of all the blades, is intuitively easier to understand because it is described in terms of the collective mode and the periodic longitudinal and lateral modes in the nonrotating frame; 2) fuselage motion and active controls couple with the rotor motion in the form of nonrotating feedback effects; and 3) the transformation to multiblade coordinates replaces some harmonic terms in the equations of motion by constants and higher frequency terms. This last property results in the time-averaged constant coefficient approximation being valid for higher advance ratios compared with the individual blade equations. It also reduces the computation time necessary for a stability analysis using Floquet theory in the case that periodic terms are not time aver aged. The method of multiblade coordinates has been applied by Hohenemser and Yin, Biggers, Gaonkar and Peters,' Hodges, Briczinski and Cooper, and others to analyze various aspects of the motion of multibladed rotors. In this Note a modified set of multiblade coordinates is introduced for which the transformation between individual blade coordinates and mutiblade coordinates is orthogonal, hence the name orthogonal multiblade coordinates. This property results in simplifications in the transformations of the equations of motion and their solutions.

It is shown that the 0(6) limit of the interacting boson model (IBA) corresponds to the γ-unstable model of Jean and Wilets, if one considers an infinite number of bosons in IBA ( N → ∞). The rigid triaxial rotor model with γ = 30° satisfies the same selection rules, but differs considerably with respect to B (E2) values and energies.

The problem of existence of periodic motions of a gyrostat is studied. The gyrostat consists of a rigid body and a rotor, the axis of which is stationary with respect to the rigid body in a central Newtonian force field. In /1,2/, Poincare's method of small parameter was used to show the existence of periodic motions of a gyrostat with a single fixed point in a central Newtonian force field. It was assumed that the gyrostat differs little from a dynamically symmetric one, and the constant gyrostatic moment was assumed to be sufficiently small. Moreover, it was assumed that the center of gravity of the gyrostat is sufficiently close to the fixed point, and the center of attraction is sufficiently far removed from the gyrostat.

It is shown that for large boson number N the O(6) group of the interacting boson model contracts to the group [R5] O(5) of the rotor with fixed deformation.

Fur elliptische Umlaufbahnen mit Exzentrizitaten nahe eins ist es moglich, mit Hilfe eines kontinuierlich verstellbaren Steuerrads Schwerkraft-Stabilisierung anzuwenden. Das Radsteuergesetz sowie die sich daraus ergebenden stabilen Gebiete sind in einer fruheren Arbeit beschrieben worden, und zwar fur den Fall eines Rads, dessen Geschwindigkeit phasenmasig mit der wirklichen Anomalie genau ubereinstimmt. In der vorliegenden Arbeit werden die sich fur verschiedene Werte der Phasenverschiebung ergebenden invarianten Flachen untersucht. Gravity gradient stabilization can be used effectively in elliptic orbits with eccentricities approaching unity by the use of a variable speed control wheel. The wheel control law and the resulting stable regions have been described in a previous paper for the case where the wheel speed is exactly in phase with the true anomaly. Here, the invariant surfaces resulting for different values of the phase shift are investigated.

It is shown that the 0(6) limit of the interacting boson model (IBA) corresponds to the γ-unstable model of Jean and Wilets, if one considers an infinite number of bosons in IBA (N→∞). The rigid triaxial rotor model with γ = 30° satisfies the same selection rules, but differs considerably with respect to B(E2)-values and energies.

A two-dimensional generalization of the one-dimensional kicked-rotor model is introduced. As in one dimension, this model can be mapped on a two-dimensional Anderson model for localization. It is found that all the states are localized in momentum space and that the localization length grows exponentially with the mean free path, as expected from the scaling theory for localization. This suggests that the correspondence between the quantum dynamics of chaotic systems and Anderson localization that was found in one dimension holds in two dimensions as well.

Time-on-target on pursuit rotor tracking tasks has been shown to decrease for triangle, square, and circle templates, respectively. Since these templates are unrelated geometric shapes they cannot be scaled along a single continuous dimension. For the present study, templates were constructed to be continuously scaled by eccentricity. It was demonstrated that time-on-target on pursuit rotor tracking was a decreasing function of template eccentricity. Also, it was concluded that elliptical templates were preferred over the usual geometric templates because time-on-target relationships among templates can be examined.

Each weight change of three spinning mechanical gyroscopes whose rotor's masses are 140, 175, and 176 g has been measured in inertial rotations without systematic errors. The experiments show that the weight changes on rotations around the vertical axis are completely asymmetrical: The right rotations (spin vector pointing downwards) cause weight decrease of the order of milligrams (weight), proportional to the frequency of rotations at 3 000--13 000 rpm. However, the left rotations do not cause any change in weight.

summary, this work confirms that the quasi-energy nearest-neighbor spacings distribution of the kicked rotor is Poissonian and therefore is similar to the corresponding dis-tribution for energy levels spacing in the one-dimensional localization problem. This is further evidence for the simi-larity between these two problems. This distribution is very different from the ones that were obtained so far for sto-chastic problems with time-independent Hamiltonians. Therelevant difference between the quantal behavior of these two classes of problems, both chaotic in their classical limit,is the extension or localization of the wave functions. Note added. After submission of this paper we learned of work by F. M. Israilev (unpublished, in Russian) which isfully consistent with ours, although the emphasis is quite different. We thank M. V. Berry for communicating thiswork to us.We thank H. G. Schuster for suggestions and encourage-ment at carly stages of this work and M. V. Berry for com-ments

For a near-rigid rotor in its undeformed state, using Cuvz floating coordinates, the inertia tensor is $$\left[ {{{I}^{R}}} \right]unde{\mkern 1mu} f = \left[ {\begin{array}{*{20}{c}} {{{A}^{R}}} & {amp;0} & {amp;0} \\ 0 & {amp;{{A}^{R}}} & {amp;0} \\ 0 & {amp;0} & {amp;{{C}^{R}}} \\ \end{array} } \right]$$ (12.1)

In many problems in engineering and physics small parameters arise in a natural way: weak coupling between modes, small damping, slow variation of coefficients in the equations corresponding with quantities in the system as mass, lenght etc. A large number of such problems can be reformulated in the following form $$ \eqalign{ & \dot {\text{ x}}\, = \, \in \,{\text{X}}\,(\phi,{\text{x)}}\, + \, \in ^{\text{2}} \,...,\,{\text{x}}\, \in \,{\text{D}} \subset \,{\text{R}}^{\text{n}} \cr & \dot \phi \, = \,\Omega {\text{(x)}}\, + \, \in \,...,\,\phi \, \in \,{\text{T}}^{\text{m}} \cr} $$ (1) with n,m e ℕ, e a small parameter and initial values for x and ϕ added.

In two previous lectures the gyroscopic system called gyrostat has been presented and two kinds of problem connected with the case of torque-free motion have been discussed. In the following we will consider the torque-free motion of the unsymmetrical gyrostat with a rotor which is not aligned with a principal axis nor does it lie in the plane of two principal axes. Since the polhodes, i.e. the intersection lines of the energy and the angular momentum ellipsoids allow a simple visualization of the motion we will start with a discussion of some interesting problems concerning the polhodes. In particular, we return to the so-called osculation problem the solution of which provides the possible states of permanent rotation. The condition for such a state of motion has already been developed.

Using numerical computations on a map which describes the time evolution of a particular mechanical system in a four-dimensional phase space (The kicked double rotor), we have found that the boundaries separating basins of attraction can have different properties in different regions and that these different regions can be intertwined on arbitrarily fine scale . In particular, for the double rotor map, if one chooses a restricted region of the phase space and examines the basin boundary in that region, then either one observes that the boundary is a smooth three-dimensional surface or one observes that the boundary is fractal with dimension d ≊ 3.9 , and which of these two possibilities applies depends on the particular phase space region chosen for examination. Furthermore, for any region (no matter how small) for which d ≊ 3.9 , one can choose subregions within it for which d = 3. (Hence d ≊ 3.9 region and d = 3 region are intertwined on arbitrarily fine scale.) Other examples will also be presented and analyzed to show how this situation can arise. These include one-dimensional map cases, a map of the plane, and the Lorenz equations. In one of our one-dimensional map cases the boundary will be fractal everywhere, but the dimension can take on either of two different values both of which lie between 0 and 1. These examples lead us to conjecture that basin boundaries typically can have at most a finite number of possible dimension values. More specifically, let these values be denoted d 1 , d 2 ,…, d N . Choose a volume region of phase space whose interior contains some part of the basin boundary and evaluate the dimension of the boundary in that region. Then our conjecture is that for all typical volume choices, the evaluated dimension within the chosen volume will be one of the values d 1 , d 2 ,…, d N . For example, in our double rotor map it appears that N = 2, and d 1 = 3.0 and d 2 = 3.9.

The open problem on whether or not the chirality exists in doublet bands M1 and M4 in light-mass even-even nucleus 60Ni is studied by adopting the recently developed fully quantal four-j shells triaxial particle rotor model. The corresponding experimental energy spectra, energy differences between doublet bands, and the available B ( M 1 ) / B ( E 2 ) values are successfully reproduced. The analyses on the basis of the angular momentum components, the azimuthal plots, and the K-plots suggest that the chiral modes exist at I ≥ 12 ħ in doublet bands M1 and M4.

Let βcI be the critical inverse temperature in an Ising ferromagnet with pair interactions and let βcR be the critical temperatures in the plane rotor (classical xy model) with the same couplings. We prove that βcR ⩾ 2βcI. This yields the lower bound βc ⩾ 0.88 for the Kosterlitz-Thouless transition.

The distribution with respect to Ray’s asymmetry parameter κ of polyatomic molecules listed in the Landolt–Borstein tables is skewed towards κ=−1 (prolate rotor limit). A plausible definition of ‘‘randomly shaped’’ objects leads to a prediction with this qualitative behavior but less strongly biased toward κ=−1 than the experimental distribution.

An analytic model for the vibration response of turbomachinery rotor blades that includes the effects of variations in blade thickness, curvature of the blade edges, and variations in the curvature of the blade middle surface in two dimensions is developed. Mathematical fits to both surfaces of the blade are generated in terms of polynomial equations with constant coefficients. The polynomial equations for the blade surfaces are then used in shell equations, based on Love's thin shell assumptions, to generate differential equations governing the vibration motion of the blade. The coefficients in the blade‐fitting polynomials act as parameters in the equations of motion for the blade, so that equations for a new blade can be developed easily by changing the coefficients in the governing equations to those generated for the new blade. An approximate method of solution for the resonant response of a sample blade is presented.

All of the contributions to the discussion recognized that the basic fallacy in Dr Aughtie's argument (Physics Bulletin November 1970 p519) lay in his first statement that the direction of net mechanical force on the rotor must be determined by the direction in which the lines of force leave it. This was illustrated most succinctly by Bloch, McCaig and Durham who pointed out that two conductors at the same potential and bearing charges of the same sign will repel one another although lines of force still leave each normally.