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Information about principal axes and moments of inertia is presented in terms of formulas involving solely quantities which can be expressed in literal form whenever central principal axes can be located by inspection for at least one state of a deformable system composed of particles and rigid bodies. Two illustrative examples are worked out in detail.
The application of the pendulum method to the experimental determination of the moments of inertia of airplanes is discussed in this report. Particular reference is made to the effects of the air, in which the airplane is immersed, on the swinging tests and to the procedure by which these effects are taken into account. This procedure has been used for some time, and the data on several airplanes for which the moments of inertia have been found are included.
Flight test maneuvers and dynamic modeling techniques were developed for determining aircraft moments of inertia from flight test data. Full nonlinear rigid-body rotational equations of motion were used in the analysis, with aerodynamic moment dependencies modeled by linear expansions in the aircraft states and controls. Aerodynamic parameters were estimated simultaneously with inertia parameters using equation-error modeling applied to flight test data from maneuvers designed specifically for this problem. The approach was demonstrated using a nonlinear F 16 simulation, then applied to a remotely-piloted subscale aircraft flight test. Errors in the aircraft moment of inertia parameters determined from simulated F-16 flight test data were less than 6 percent compared to the true values in the simulation. Flight test results for the subscale aircraft were within 6 percent of ground-test values obtained using the same aircraft.
An approximation method is presented for reducing a nonlinear differential equation (for the 'weather vaning' motion of a wind turbine) to an equivalent constant moment of inertia problem. The integrated average of the moment of inertia is determined. Cycle time was found to be the equivalent cycle time if the rotating speed is 4 times greater than the system's minimum natural frequency.
Flight test maneuver design and dynamic modeling techniques were developed for determining aircraft moments of inertia from flight test data. Full nonlinear rigid-body rotational equations of motion were used in the analysis, with aerodynamic moment dependencies modeled by linear expansions in the aircraft states and controls. Aerodynamic parameters were estimated simultaneously with inertia parameters using equation-error modeling applied to flight test data from maneuvers designed specifically for this problem. The approach was demonstrated using a nonlinear F 16 simulation, then applied to a remotely piloted subscale aircraft flight test. Errors in the aircraft moment of inertia parameters determined from simulated F-16 flight test maneuver data were less than 6 percent compared to the true values in the simulation. Flight test results for the subscale aircraft were within 6 percent of ground-test values obtained using the same aircraft.
Flight test maneuver design and dynamic modeling techniques were developed for determining aircraft moments of inertia from flight test data. Full nonlinear rigid-body rotational equations of motion were used in the analysis, with aerodynamic moment dependencies modeled by linear expansions in the aircraft states and controls. Aerodynamic parameters were estimated simultaneously with inertia parameters using equation-error modeling applied to flight test data from maneuvers designed specifically for this problem. The approach was demonstrated using a nonlinear F-16 simulation, then applied to a remotely-piloted subscale aircraft flight test. Errors in the aircraft moment of inertia parameters determined from simulated F-16 flight test maneuver data were less than 6 percent compared to the true values in the simulation. Flight test results for the subscale aircraft were within 6 percent of ground-test values obtained using the same aircraft.
The rotational dynamics of a body are governed by the values of its principle moments of inertia. These quantities are not directly observable, but they are related to the harmonic coefficients of the external gravity field and to the density distribution within the body, both of which can be inferred from appropriate observations. It is shown that, for the particular case of a spherical planet whose density varies as a power of the radial distance, the principal moment of inertia has an elegantly simple form. Application of this simplified case to the Jovian planets suggests that the density profiles outside the central core are approximately linear, with the apparent exception of Neptune.
A recent value found by Nordtvedt and Will (1972) for the rate of increase of the moment of inertia of earth resulting from a decreasing G is shown to be based on conflicting physical assumptions. The corrected result for this restricted problem yields a rate of change almost twice as large. However, in a realistic treatment, additional purely geophysical causes must also be taken into account, and these imply a decreasing moment of inertia on a scale much outweighing the increase that would occur for any acceptable value of the derivative of G. This accords with the intrinsic acceleration of angular velocity established from ancient-eclipse data.
Earth-orbiting spacecraft often contain solar arrays or antennas supported by a preloaded mast. Because of weight and cost considerations, the structures supporting the spacecraft appendages are extremely light and flexible; therefore, it is vital to investigate the influence of all physical and structural parameters that may influence the dynamic behavior of the overall structure. The study primarily focuses on the mast for the space station solar arrays, but the formulations and the techniques developed in this study apply to any large and flexible mast in zero gravity. Furthermore, to determine the influence on the circular frequencies, the mass moment of inertia of the mast was incorporated into the governing equation of motion for bending. A finite element technique (MSC/NASTRAN) was used to verify the formulation. Results indicate that when the mast is relatively flexible and long, the mass moment inertia influences the circular frequencies.
Determination of mass, shape, moments of inertia, and gravitational field of the moon
The buckling failure conditions for a bar with nonprogressively variable moment of inertia J(sub n), although constant over length l(sub n), are developed.
It is pointed out that the observed moments of inertia of the moon, disclosed by its librations, are influenced mainly by the distribution of mass in the outer zone in which the lithostatic pressure is less than 10 kb (i.e., in the outer shell not more than 200 km deep); a conspicuous departure of such moments from those expected in hydrostatic equilibrium disclosed that these layers could never have been fluid. In the same way, the actual shape of the lunar surface cannot represent a solidified surface of a fluid, petrified at any distance from the earth. The shape of the moon and differences of its moments of inertia must reflect the way in which the initial process of cold accretion fell short of producing a globe with strictly spherically-symmetrical stratification of material. Such melting or lava flows as may have occurred at the moon's surface from time to time must have remained localized, and without much effect on the dynamical properties of the moon.
We have investigated the influences of lateral variations of viscosity on the moment of inertia tensor from viscous flows due to the density anomalies in the mantle inferred from seismic tomographic models. The scaling relations between the density and the seismic anomalies is taken as either a constant or a function increasing with depth in accord with the recent high-pressure experimental studies. The viscosity is taken as an exponential function of the 3D density anomaly. In models with an isoviscous background, the effects on the perturbed moment of inertia tensor from the lateral viscosity variations are smaller than those due to variations in the radial viscosity profiles. In mantle models with a background viscosity increasing with depth, the influences of the lateral viscosity variations are significant. The most striking feature in the latter case is that the two off-diagonal elements delta I(sub xz) and delta I(sub yz) in the inertia tensor exhibit greatest sensitivity to lateral variations of the viscosity. While the other elements of the inertia change by only about a few tens of percent in the range of lateral viscosity contrast considered (less than 300), delta I(sub xz) and delta I(sub yz) can vary up to 40 times even with a change in sign, depending on the radial viscosity stratification and the location of the strongest lateral variations. The increase in the velocity-density scaling relation with depth can reduce the influences of the lateral viscosity variations, but it does not change the overall sensitive nature of delta I(sub xz) and delta I(sub yz). This study demonstrates clearly that the lateral viscosity variations, especially in the upper mantle, must be considered in the determination of long-term polar wander, since the variations in the delta I(sub xz) and delta I(sub yz) terms are directly responsible for exciting rotational movements.
Moment of inertia and damping in baffled and nonbaffled cylindrical tanks
A strategy for determining an improved lunar moment of inertia is proposed. An improved uncertainty in the lunar inhomogeneity parameter could reduce the core density error from 4.20 gr/cu cm to 0.1 gm/cu cm for the case of a lunar density model having a 300 km core radius. The current error of 0.0025 for the lunar inhomogeneity parameter is mostly due to the uncertainties in the C20 and C22 gravity harmonics. An optimum reduction strategy for obtaining an order of magnitude improvement in the gravity estimates is based on covariance analyses of Doppler data. The long-arc reduction method is shown to provide better results than the short-arc technique, and the use of an orbit with a 7000 km semimajor axis along with certain terms of up to degree and order eight is recommended.
In a recent Technical Note (NACA-TN-115, October, 1922), Norton and Carrol have reported experiments showing that a relatively large (15 per cent) increase in longitudinal moment of inertia made no noticeable difference in the stability of a standard SE-5A airplane. They point out that G. P. Thomson, "Applied Aeronautics," page 208, stated that an increase in longitudinal moment of inertia would decrease the stability. Neither he nor they make any theoretical forecast of the amount of decrease. Although it is difficult, on account of the complications of the theory of stability of the airplane, to make any accurate forecast, it is the purpose of this report to attempt a discussion of the matter theoretically with reference to finding a rough quantitative estimate.
The objective of this research effort is to determine the most appropriate, cost efficient, and effective method to utilize for finding moments of inertia for the Uninhabited Aerial Vehicle (UAV) Dryden Remotely Operated Integrated Drone (DROID). A moment is a measure of the body's tendency to turn about its center of gravity (CG) and inertia is the resistance of a body to changes in its momentum. Therefore, the moment of inertia (MOI) is a body's resistance to change in rotation about its CG. The inertial characteristics of an UAV have direct consequences on aerodynamics, propulsion, structures, and control. Therefore, it is imperative to determine the precise inertial characteristics of the DROID.
The objective of this research effort is to determine the most appropriate, cost efficient, and effective method to utilize for finding moments of inertia for the Uninhabited Aerial Vehicle (UAV) Dryden Remotely Operated Integrated Drone (DROID). A moment is a measure of the body's tendency to turn about its center of gravity (CG) and inertia is the resistance of a body to changes in its momentum. Therefore, the moment of inertia (MOI) is a body's resistance to change in rotation about its CG. The inertial characteristics of an UAV have direct consequences on aerodynamics, propulsion, structures, and control. Therefore, it is imperative to determine the precise inertial characteristics of the DROID.