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The elastic deformation of a spinning sphere is calculated from first principles. Numerical results are quoted for a quartz sphere spinning at 200 Hz, the most likely configuration for the relativity gyro experiment. The difference in principal moments of inertia is also calculated for the spinning gyro.
Two formulations of the oblique wing flutter problem are presented: one formulation allows wing bending deformations and the rigid body roll degree of freedom while the second formulation includes bending-torsional deformation and roll degrees of freedom. Flutter is found to occur in two basic modes. The first mode is associated with bending-roll coupling and occurs at low reduced frequency values. The other instability mode is primarily one of classical bending-torsion with negligible roll coupling; this mode occurs at much higher reduced frequencies. The occurrence of bending-roll coupling mode leads to lower flutter speeds while the bending-torsion mode is associated with higher flutter speeds. The ratio of the wing mass moment of inertial in roll to the fuselage moment of inertia evidently plays a major role in the determination of which of the two instabilities is critical.
Theoretical analysis and experimental investigations are presented for two deployment concepts of the drogue parachute deployment for the space shuttle solid rocket booster. The analysis represents the motion of three coupled rigid bodies, with one of the bodies having variable mass and moment of inertia. The unfurling process of the parachute from the bag is idealized as the flow of a continuum out of a control surface. The pilot parachute or tethered nose cap is modeled as a flexible pendulum with a nonlinear spring and a moving support. Measured wind tunnel test data compare reasonably well with the theory.
The current state of knowledge concerning the regional geology and geophysics of Mars is summarized. Telescopic observations of the planet are reviewed, pre-Mariner models of its interior are discussed, and progress achieved with the Mariner flybys, especially that of Mariner 9, is noted. A map of the Martian geological provinces is presented to provide a summary of the surface geology and morphology. The contrast between the northern and southern hemispheres is pointed out, and the characteristic features of the surface are described in detail. The global topography of the planet is examined along with its gravitational field, gravity anomalies, and moment of inertia. The general sequence of events in Martian geological history is briefly outlined.
The offset of the center of mass of the moon from its center of figure together with moment of inertia differences are explainable by a lunar crust of randomly varying thickness. The necessity of postulating a method of preferential material transport into a particular lunar hemisphere to explain the lunar asymmetry is eliminated.
The dynamics and stability of a spin stabilized spacecraft with a hinged appendage system are treated analytically and numerically. The hinged system consists of a central hub with masses attached to massless booms of fixed length whose orientation relative to the main part can change. The equations of motion for the hinged system, with viscous damping at both hinge points, are linearized about the nominal equilibrium position where the booms are orthogonal to the nominal spin axis. Analytic stability criteria indicate that hinge damping must be present and that for limiting cases, where the spin axis is an axis of symmetry, certain conditions relating the hinge point offset coordinates to the moment of inertia ratio and end masses must be satisfied. The hinge damping is always required for the nominal deployment of hinge members.
Dynamic model tests were staged to compare the aeroelastic stability of a free-flying oblique-winged aircraft and the known divergent instability characterizing swept-forward wing configurations, to test the effect of wing elasticity on aileron control and trim. The aircraft fuselage was clamped in some tests and left free to roll in others. Two rigid wing panels were hinged near the wing center with elastic restraining springs. It is found that the aeroelastic divergence affecting swept-forward wings does not occur with an oblique wing, whose aeroelastic instability sets in at a dynamic pressure exceeding that for static divergence of swept-forward wings, and appears in the form of undamped oscillations. Oblique wing stability is sensitive to the moment of inertia of the fuselage in roll. Roll control and lateral trim are attainable with conventional ailerons, even at speeds at which divergence of a clamped forward wing shows up.
Very long base line interferometry (VLBI) observations of lunar radio transmitters have been combined with data from laser ranging to lunar retroreflectors to estimate simultaneously (1) parameters in models of the lunar orbit and libration and (2) the selenodetic coordinates of the radio transmitters and retroreflectors. For the ratio of the mass of the sun to that of the earth plus moon, a value of approximately 328,900.5 is obtained. The lunar moment-of-inertia ratios beta and gamma are also determined. The values and most of the uncertainties obtained for the third-degree harmonics of the moon's gravity field are comparable to those which have been obtained by others from observations of lunar-orbiting spacecraft. However, the results for the two third-degree gravity coefficients have much less uncertainty than determinations based on laser data alone. For the relative position vectors of the lunar radio transmitters and the retroreflectors, the estimates have uncertainties of about 30 m along the earth-moon direction and about 10 m in each of the two transverse coordinates.
The velocity and attenuation structure of the moon below the crust is examined using surface events. The moon is divided into an upper mantle and a lower mantle, the division at a depth of about 500 km being marked by a reflector identified on polarization filtered record sections. The upper mantle has a P-wave velocity of about 8 km/sec, a Poisson's ratio of about 0.25 and a Q for P waves of about 5000. This region contains no partial melt and is depleted in volatiles, notably water. The lower mantle has a lower S-wave velocity and probably a lower P-wave velocity than the upper mantle, with a Poisson's ratio of about 0.34. The lower mantle has a Q for P waves of approximately 1500, substantially lower than the upper mantle but probably still high enough to preclude partial melting. The velocity structure and the current value of the moment of inertia factor indicate an increase of density below about 500 km, perhaps due to an increase in iron content. We do not have any information directly pertaining to seismic velocities below 1000 km depth.
The paper investigates the hypothesis that the asymmetry of the moon with respect to the distribution of maria, reflected in that the surface area of the moon covered by mare material is far greater on the earth-facing side than on the far side, is due to the action of the earth's gravity at a time when the moon was less distant from the earth than today. Such conditions would lead to gravitationally favored areas on the moon such that mare basalt magmas might erupt preferentially on the front side of the moon. Gravitational asymmetry is also discussed in terms of its effect on the shape of the moon, its center of mass, its moments of inertia, and the time scale for the evolution of its orbit.
Recent advances in the theory of rotation are combined with traditional approaches to study the rotational evolution of the 33 known natural satellites. A calculation similar to that reported by Burns and Safronov (1973) is applied to each satellite to obtain the characteristic time of decay of any wobble motion to smooth rotation about the principal axis of maximum moment of inertia. Stability criteria and capture probabilities are calculated for the 3/2 spin resonance. Results show that only the regular satellites and Iapetus, Hyperion, Triton, and the moon are tidally evolved. Of these, 13 have confirmed synchronous rotation periods; capture probabilities into the 3/2 resonance indicate that none of the remaining 10 should be captured in nonsynchronous, commensurate spin states. For the most part, the irregular satellites retain their original spins except for a relaxation to principal axis rotation. Tidal evolution of the obliquities of the satellites is evaluated in the framework of the generalization of Cassini's laws for the moon. Nearly resonant, forced librations in longitude of 4.8 and 0.5 deg are calculated on the basis of the observed shapes of Phobos and Deimos, respectively.
Many of the properties of the Moon, including the enrichment in Ca, Al, Ti, U, Th, Ba, Sr, and the REE and the depletion in Fe, Rb, K, Na, and other volatiles can be understood if the Moon represents a high-temperature condensate from the solar nebula. Thermodynamic calculations show that Ca-, Al-, and Ti-rich compounds condense first in a cooling nebula. The initial high temperature mineralogy is gehlenite, spinel, perovskite, Ca-Al-rich pyroxenes, and anorthite. Inclusions in carbonaceous chondrites such as the Allende meteorite are composed primarily of these minerals and, in addition, are highly enriched in refractories such as REE relative to carbonaceous chondrites. These inclusions can yield basalt and anorthosite in the proportions required to eliminate the europium anomaly, leaving a residual spinel-melilite interior. A deep interior high in Ca-Al does not imply an unacceptable mean density or moment of inertia for the Moon. The inferred high-U content of the lunar interior, both from the Allende analog and the high heat flow, indicates a high-temperature interior. The model is consistent with extensive early melting, with shallow melting at 3 AE, and with presently high deep internal temperatures. It is predicted that the outer 250 km is rich in plagioclase and FeO. The low iron content of the interior in this model raises the interior temperatures estimated from electrical conductivity by some 800 C.
Information theory can develop a technique which takes experimentally determined numbers and produces a uniquely specified best density model satisfying those numbers. A model was generated using five numerical parameters: the mass of the earth, its moment of inertia, three zero-node torsional normal modes (L = 2, 8, 26). In order to determine the stability of the solution, six additional densities were generated, in each of which the period of one of the three normal modes was increased or decreased by one standard deviation. The superposition of the seven models is shown. It indicates that current knowledge of the torsional modes is sufficient to specify the density in the upper mantle but that the lower mantle and core will require smaller standard deviations before they can be accurately specified.
A computer program was developed for the rapid computation of the mass properties of complex structural systems. The program uses rigid body analyses and permits differences in structural material throughout the total system. It is based on the premise that complex systems can be adequately described by a combination of basic elemental shapes. Simple geometric data describing size and location of each element and the respective material density or weight of each element were the only required input data. From this minimum input, the program yields system weight, center of gravity, moments of inertia and products of inertia with respect to mutually perpendicular axes through the system center of gravity. The program also yields mass properties of the individual shapes relative to component axes.
The present paper argues for using the information theory approach as an inference technique in solid earth geophysics. A spherically symmetric density distribution is derived as an example of the method. A simple model of the earth plus knowledge of its mass and moment of inertia leads to a density distribution. Future directions for the information theory approach in solid earth geophysics as well as its strengths and weaknesses are discussed.
An aircraft capable of transporting containerized cargo over intercontinental distances is analyzed. The specifications for payload weight, density, and dimensions in essence configure the wing and establish unusually low values of wing loading and aspect ratio. The structural weight comprises only about 18 percent of the design maximum gross weight. Although the geometric aspect ratio is 4.53, the winglet effect of the wing-tip-mounted vertical tails, increase the effective aspect ratio to approximately 7.9. Sufficient control power to handle the large rolling moment of inertia dictates a relatively high minimum approach velocity of 315 km/hr (170 knots). The airplane has acceptable spiral, Dutch roll, and roll-damping modes. A hardened stability augmentation system is required. The most significant noise source is that of the airframe. However, for both take-off and approach, the levels are below the FAR-36 limit of 108 db. The design mission fuel efficiency is approximately 50 percent greater than that of the most advanced, currently operational, large freighter aircraft. The direct operating cost is significantly lower than that of current freighters, the advantage increasing as fuel price increases.
A technique is described, by which a glass strip may be bent to match any curve of large radius of curvature, to a high degree of accuracy, so that it may be used as a glancing incidence X-ray or extreme ultraviolet optical element. The desired match is obtained by applying the optimum combination of end couples and by varying the cross-sectional moment of inertia along the length of the strip. A particular case, that of a parabola for use as a laboratory X-ray collimator, is considered in detail. The analysis predicts that a collimation of one or two arc seconds should be obtainable in practice, with simple and inexpensive apparatus. A prototype collimator to be used for the testing of space payloads using geometric (McGrath) collimators is described and laboratory results presented.
Theoretical seismic properties of the planet Mars are investigated on the basis of the various models which have been proposed for the internal composition of the planet. The latest interpretation of gravity-field data, assuming a lower value of the moment of inertia, would require a less dense mantle and a larger core than previous models. If Mars is chondritic in composition, the most reasonable models are an incompletely differentiated H-chondrite or a mixture of H-chondrites and carbonaceous chondrites. Seismic profiles, travel times, and free oscillation periods are computed for various models, with the aim of establishing which seismic data is crucial for deciding among the alternatives. A detailed discussion is given of the seismic properties which could - in principle - help answer the questions of whether Mars' core is liquid or solid and whether Mars has a partially molten asthenosphere in its upper mantle.