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In the northern Sargasso Sea, recent continuous vertical profiles horizontal velocity and sound speed have revealed strong current shears of large horizontal extent and of inertial frequency in regions of low sound‐speed gradient. The influence of shear on ray paths is particularly evident in restricted regions in which the sound‐speed‐gradient is smaller than the current shear. Stability considerations pertaining to stratified shear flow suggest that shear refraction is most likely to be of importance when the ratio of the vertical gradient of sound speed (CZ) and the Brunt‐Vaisala frequency (N) is of order one. A simple model illustrates that rays emitted or vertexing within a layer of large shear, but small sound‐speed gradient, will be significantly refracted. Moreover, since the interaction is not isotropic, the reciprocity theorem does not apply and the effects of shear on ray paths are dependent on the direction of the ray with respect to the current.

Algorithms for failure detection, isolation, and correction of redundant inertial instruments in the strapdown dodecahedron configuration are competitively evaluated in a digital computer simulation that subjects them to identical environments. Their performance is compared in terms of orientation and inertial velocity errors and in terms of missed and false alarms. The algorithms appear in the simulation program in modular form, so that they may be readily extracted for use elsewhere. The simulation program and its inputs and outputs are described. The algorithms, along with an eight algorithm that was not simulated, also compared analytically to show the relationships among them.

Future space exploration may involve communications between spacecraft moving at relativistic velocities. One of the significant problems associated with such communication is spectral distortion of signals which are propagated between relativistic frames. This distortion is generated by both changing propagation distances and purely relativistic electromagnetic field transformations. In this paper a linear integral transformation is formulated for relating the Fourier spectra of the source antenna excitation current and the resulting incident electric field at the receiving antenna. The kernel of the transformation is evaluated for the case of a steerable source antenna tracking on the advanced receiver position. The transformation is then applied to the case of an ideal thin-wire half-wave dipole source antenna excited by a narrowband, double-sideband modulated current. The specific distortions of spectral spreading and translation are then related to increased bandwidth and upper cutoff frequency requirements of receiving systems in relativistic applications.

A method for computing and displaying the temporal variation of rotary spectral estimates is described. The method is applied to time series measurements of highly nonstationary winds and currents. The results indicate approximately fortnightly modulation of diurnal wind energy and inertial current energy.

A general analytic solution is obtained for the development of a neutral planetary boundary layer (PBL) excited by an interior flow that has a negligible inertial acceleration, but has an arbitrary temporal acceleration. The solution corresponding to one particular class of interior flows indicates that a singular PBL response similar to the so-called “critical-latitude effect” would occur only if the pressure gradient force is negligible compared to the Coriolis force and temporal acceleration. The critical-latitude effect may then be interpreted as an inertial resonance in a negative sense. While this is a sufficient condition for giving rise to the critical-latitude effect, whether or not it is also a necessary condition remains to be determined. The PBL excited by a propagating wave in the meridional velocity component embedded in an easterly zonal velocity is investigated numerically. A large range of inertial as well as temporal accelerations is examined. The wave component of the PBL respo...

The nonlinear dynamics of inertial-gravity and Rossby waves are studied via the asymptotic method of multiple scales. Two important parameters which enter the problem are the conventional Rossby number ϵ and a nondimensional measure of the northward variation of the Coriolis parameter μ. Restricted to the weakly nonlinear limit (ϵ≪1), this paper examines three possible nonlinear wave motions: weakly non-linear interactions on an f-plane (μ=0), very weakly interacting disturbances in a quiescent atmosphere [ϵ=O(μ2)], and nonlinear interactions of finite-amplitude disturbances [ϵ=O(μ)]. In particular, resonant interactions are studied and the slow modulations of the linear solutions due to the nonlinearity are found. Some of these nonlinear solutions are unstable, being able to feed their energy into a resonantly interacting pair of disturbances.

The deposition of aerosol particles on swarms of accelerating spherical glass beads was studied over a range of aerosol particle sizes and air velocities, and two glass bead sizes. The results were interpreted by a theoretical model which was based on equations valid for inertial impaction and interception of spheres on single, stationary spheres, and which included an empirical factor dependent on the volumetric concentration of the collection particles.

Energy spectra of high–altitude atmospheric turbulence data were analyzed. Kolmogorov's similarity theory for the inertial subrange was applied to infer energy dissipation rates from the spectra. The dissipation rates increase as the third power of the truncated root-mean-square values of turbulence: thus, the former can be inferred directly from the later with relative case. In the stratosphere the dissipation rates can occasionally he of the same order as those in the surface layer; a single curve can hardly represent the dissipation state in the atmosphere.

As a meandering current changes its curvature vorticity, the lateral shear, the shearing deformation, the vertical shear, and the lateral temperature gradient also change. Changes in these parameters, together with their generating and conversion mechanisms, are called the turning process. The objectives are first to identify, in a situation where friction is negligible, the pertinent generating and conversion mechanisms generally, and second to assess their relative importance in the turning process for high-speed inertial currents with horizontal meander scales small compared to the radius of the earth. A conclusion is that in the dynamics of these high-speed currents, where vertical motion plays a central role, the beta effect is negligible. Instead, the turning process is dominated by the banking and the divergence mechanisms. The current banks as it turns and converts curvature vorticity to lateral shear vorticity. As a striking consequence of this conversion, the speed axis migrates lateral...

Rotational analyses have been carried out for the three longest wavelength bands observable in the '2900 Å system' of SO2 (at 3340, 3359, and 3395 Å). Although the bands are perturbed quite severely it has been possible to prove that they are type C bands, and that the approximate upper state geometric structure of the molecule is r(S—O) = 1.53 Å, [Formula: see text]. Comparison with the theoretical calculations of Hillier and Saunders now leaves little doubt that the upper electronic state is the π → π* 1A2 state, appearing in absorption by Herzberg–Teller mixing through Q3′(b2), as recently proposed by Dixon and Hallé. A vibrational numbering for these bands is given, which is consistent with the inertial defect obtained from the rotational analysis, and with recent isotope data published by Brand and Nanes: the 3395 Å band appears to be 031–000, and the electronic origin falls near 27 930 cm−1.

The Inertial Reference Unit (IRU) used in NASA's Orbiting Astronomical Observatory (OAO-C or Copernicus) uses three single degree of freedom, floated, rate-integrating gyros operated in binary, pulse-restrained torque loops to provide an inertial attitude reference for the spacecraft's altitude control system. Since 21 August 1972 when the spacecraft was launched, more than 15,000 hours of continuous and troublefree operation have been accumulated on the IRU. When prelaunch operation is included, the running times for the gyro wheels range between 17,000 and 22,000 hours. The drift rates observed on these inertial grade gyros during the 1½ year of in-orbit operation have remained within a band of 16 arcsec per hour peak-to-peak When the effects of known disturbances are considered, the standard deviation of drift rate appears to approach one arcsec per hour (≤10−7 degrees per second). Included in this paper are a brief description of the OAO and IRU, a summary of the data reduction programs used to calibrate the IRU in orbit, and some thoughts on how gyros with good long-term drift stability could be applied to future spacecraft such as the Large Space Telescope and Earth Observatory Satellite.

Stewartson [5] considered second class oscillations in a spherical shell in the presence of a toroidal magnetic field. He followed Hide [2] and supposed the toroidal field to be uniform.

A 50-day time series was obtained from a current meter mooring in the Florida Current off Miami. The results agree with earlier observations regarding the significance of several-day oscillations in the Gulf Stream. The energy spectrum of the V component shows a pronounced peak at periods of 5–6 days with an amplitude of about 20 cm sec−1. Quantitatively the results are reminiscent of barotropic shelf waves, although definite conclusions about the occurrence of such waves require additional observations. Analysis of tidal fluctuations shows that 25% of the variance in the V component and 6% of the variance in the U component can be accounted for by the four major constituents, M2, S2, K1 and O1. The largest constituent in the V component is the O1 tide, whereas the K1 tide dominates in the U component. The results are in good agreement with earlier observations from the sea surface, indicating that the vertical structure of the tides is predominantly barotropic.

9 Kocher, K., "Eine lineare Theorie der Optimierungsprobleme bei Raketen mit Kleinem Schub," Dissertation, 1971, Eidgenoessische Technische Hochschule, Zurich, Switzerland. 10 Sundman, K. F., "Memoire sur le Probleme des Trois Corps," Ada Mathematica, Vol. 36, 1912, pp. 105-179. 11 Sperling, H., "Computation of Keplerian Conic Sections," ARS Journal, Vol. 31, 1961, pp. 660-661; and private communications. 12 Burdet, C. A., "Le Mouvement Keplerien et les Oscillateurs Harmoniques," J fur die reine u. angewandte Mathematik, Vol. 238, 1969. 13 Bryson, A. E. and Ho, Y.-C, Applied Optimal Control, Blaisdell, Waltham, Mass., 1969. 14 Czuchry, A. J. and Pitkin, E. T., "Regularization in Optimal Trajectory Problems," AIAA Journal, Vol. 6, No. 6, June 1968, pp. 1209-1210. 15 Sperling, H. J., "The Collision Singularity in a Perturbed TwoBody Problem," Celestial Mechanics, Vol. 7, 1969, pp. 213-221. 16 Baumgarte, J., "Numerical Stabilization of the Differential Equations of the Keplerian Motion," Celestial Mechanics, Vol. 5, 1972, pp. 490-501. 17 StumpfT, K., Himmelsmechanik, VEB, Verlag, Berlin, 1959. 18 Lewallen, J. M. et al., "Coordinate System Influence on the Regularized Trajectory Optimization Problem," Journal of Spacecraft and Rockets, Vol. 8, No. 1, Jan. 1971, pp. 15-20. 19 Tapley, B. D., "Regularization and the Calculation of Optimal Trajectories," Celestial Mechanics, Vol. 2, 1970, pp. 319-333.

The existence and first order asymptotic approximation of a one-parameter continuum of periodic orbits of the second species of Poincare are established in this paper for small values of the mass ratio. Denumerably many of these orbits are shown to be periodic in both rotating and inertial coordinates.

A strapdown system is considered as an unaided inertial navigator aboard an aircraft. Presented here are simulation results detailing the propagation of navigation errors (in nautical miles) due to strapdown sensor errors for four trajectories. They indicate the type of performance that can be expected from a strapdown system utilizing good ?off the shelf? gyros and accelerometers, and dramatically illustrate the improvements necessary in these components to obtain navigation performance comparable to that available from a good gimballed inertial system. The total navigation error for each trajectory is broken down to show the contribution from each of the various error sources. This breakdown quickly reveals which are the critical error sources for a given trajectory class, and also points up the relationship that exists between each individual error source, aircraft maneuvers, and the resulting navigation error. Several of the error mechanisms are discussed at length and a set of linearized differential equations which can be used to analyze error propagations is presented. These results should be of particular interest to the system designer who is faced with the problem of specifying the sensor error parameters necessary to meet mission performance requirements. With an analysis similar to the one presented here, but structured around his own expected mission trajectories, the designer should be able to confidently predict system accuracies and intelligently perform tradeoffs on the critical system parameters.

Inertial and interceptive impaction of spherical particles on circular cylinders was investigated theoretically. The particles were considered to be suspended in a fluid moving steadily through a random array of parallel cylinders. Fluid flow fields around the cylinders were obtained by numerically solving the Navier-Stokes Equations subject to Kuwabara's zero vorticity boundary condition. These solutions were subsequently utilized in calculating particle trajectories and impaction efficiencies. The latter are presented as functions of Reynolds number (0·2 ⩽ Rec ⩽ 40), particle inertial parameter (0 ⩽ P ⩽ 1000), particle to cylinder size ratio (0·001 ⩽ K ⩽ 1·0) and cylinder concentration (10−4 ⩽ c ⩽ 0·111). The impaction efficiencies and critical inertial parameters differ from earlier theoretical predictions. The discrepancies are primarily attributable to the inaccurate flow field representations used by previous authors. The agreement between Subramanyam and Kuloor's experimental work and present theory is satisfactory.

A theoretical study of the capillarity-induced rounding of a nearly spherical surface of revolution is presented. The material inside and/or outside this surface is considered as highly viscous Navier-Stokes liquid and the conditions that the inertial and gravity terms of the corresponding constitutive equation are negligible compared to the viscosity term are employed. Three special cases of material arrangement with respect to the dividing surface are investigated: (i) a particle in nonviscous medium, (ii) a cavity in a viscous continuum and (iii) a viscous inhomogenity in a viscous continuum. Equations for velocity and pressure distribution within and around the surface subject to rounding and that for its relaxation to sphere are derived.

The problem of proper placement of the inertial sensors to optimize system performance is important to system designers. This is especially true of redundant strapdown systems that employ more sensors than the conventional, mutually orthogonal sets of three. In systems designed for a free fall environment and with no preferred direction, such as for spacecraft attitude reference, the sensor input axes should divide the three-space equally, and can thus be viewed as being normal to the faces of regular polyhedra.' In Earth-bound inertial navigators, the effect of gravity-dependent sensor errors and the generally reduced effect of azimuth errors on navigation accuracy significantly alter the situation. Both effects tend to decrease sensor elevation angles in an optimized system. Formulas are derived and curves are drawn for optimum sensor elevation and azimuth angles vs a 0-sensitive sensor error parameter, and a mission relative azimuth error parameter. Tetrad, pentad, and hexad arrays are analyzed, affording a dramatic improvement in accuracy as well as autonomous fault isolation and/or detection capability.

The horizontal coherence of inertial oscillations was investigated using the records from six current meters moored on the Oregon continental shelf and whose separation distance varied from approximately 9 to 35 km. The rotary component method for analyzing vector time series was used to form the cross spectra and coherencies for 15 pairs of records, the length of which varied from 10 to 27 days. The velocity field was found to be highly coherent for periods greater than about 10 days. The coherencies at the inertial frequency, which were generally quite low, could be accounted for (with some exceptions) by a consideration of both the separation distance and a simple representation of the effects of stratification.

The problem of an unsteady potential flow past a group of stationary spheres is considered using the methods of images. The problem is formulated so that the number and location of the spheres is arbitrary so long as there is no overlap between adjacent spheres. Inertial and lift coefficients are determined for several different sphere arrangements. The inertial coefficient for a sphere can vary in either direction from its isolated-sphere value of 1·5. The controlling factors on this variation are the relative geometric position of the sphere within the group and its distance from its neighbors. These same factors determine, as is expected, the lift-coefficient values. In some example configurations, there is even a drag-type force generated on an individual sphere in the potential flow.

To each bounded operator C on the complex Hilbert space H \mathcal {H} we associate the vector space K C {\mathcal {K}_C} consisting of those x ∈ H x \in \mathcal {H} for which C n x → 0 {C^n}x \to 0 as n → ∞ n \to \infty . We let α ( C ) \alpha (C) denote the dimension of the closure of K C {\mathcal {K}_C} and we set β ( C ) = dim ⁡ ( K C ⊥ ) \beta (C) = \dim (\mathcal {K}_C^ \bot ) . Our main theorem states that if H is Hermitian and if H − C ∗ H C H - {C^ \ast }HC is positive and invertible then α ( C ) ≤ π ( H ) , β ( C ) = ν ( H ) \alpha (C) \leq \pi (H),\beta (C) = \nu (H) , and β ( C ) ≥ δ ( H ) \beta (C) \geq \delta (H) where ( π ( H ) , ν ( H ) , δ ( H ) ) (\pi (H),\nu (H),\delta (H)) is the inertia of H. (That is, π ( H ) = dim ( Range E [ ( 0 , ∞ ) ] ) \pi (H) = \dim \;({\text {Range}}\;E[(0,\infty )]) ) where E is the spectral measure of H; ν ( H ) = π ( − H ) \nu (H) = \pi ( - H) ; and δ ( H ) = dim ⁡ ( Ker H ) \delta (H) = \dim ({\operatorname {Ker}}\;H) .) We also show (l) that in general no stronger conclusion is possible, (2) that, unlike previous inertia theorems, our theorem allows 1 to lie in σ ( C ) \sigma (C) , the spectrum of C, and (3) that the main inertial results associated with the hypothesis that Re ⁡ ( H A ) \operatorname {Re} (HA) is positive and invertible can be derived from our theorem. Our theorems (1) characterize C in the extreme cases that either π ( H ) = 0 \pi (H) = 0 or ν ( H ) = 0 \nu (H) = 0 , and (2) prove that α ( C ) = π ( H ) , β ( C ) = ν ( H ) , δ ( H ) = 0 \alpha (C) = \pi (H),\beta (C) = \nu (H),\delta (H) = 0 if either 1 ∉ σ ( C ) 1 \notin \sigma (C) or β ( C ) > ∞ \beta (C) > \infty .

Initial alignment of gyrostabilized platforms is accomplished by gyrocompassing techniques. These cannot be used in the case of strap-down systems (gimballess inertial navigation systems) where the inertial components are "hard mounted." A scheme is proposed whereby initial alignment is accomplished for a strap-down system at standstill, using the gimballess inertial navigation system components only.

An implication of the Lorentz contraction is explored. Texts of special relativity show that a meter stick in an appropriate inertial frame is sufficiently contracted to be entirely contained in a match box. It is shown that with an appropriately transparent match box and sufficient technology, an observer at rest with respect to the match box could obtain a photograph recording the meter stick as entirely contained in the match box. A photograph taken at this spot at the same time by an observer in the inertial frame of the meter stick (or any other) also shows the meter stick overlapped at both ends of the match box. The analysis is valid for all distances between match box and observer.

The fundamental problem of inertial navigation, double integration of acceleration to obtain position, is defined and discussed. Mechanizations of both space-stable and local-vertical platform systems are exhibited. The synthesis problem for an electrically suspended gyro (ESG) strapdown system is defined and discussed: readout, readout errors due to vehicle motion, synchronization of readout with system computer, alignment, correction and calibration for mass unbalance drift, and digital mechanization. Alignment, calibration, and acceleration measurement are also discussed. Sources of error involved in the electronic gimbaling including those peculiar to strapdown configuration are discussed and compared to mechanically gimbaled systems. Advanced developments required in the component and systems areas are listed, and it is shown that such development will lead to reduced complexity, higher accuracy, and increased reliability and utility for inertial systems.

Equations are analyzed which yield a closer approximation to the inertial terms in the conventional equations of hydrodynamics by accounting for the angular velocities correlation in adjacent volume elements. Both an Isotropic and an anisotropic fluid are considered.

Measurements of ocean currents were made in the Western Mediterranean Sea at five depths for two months during early 1969. The data are of particular interest in that they show a dominant and persistent presence of inertial oscillations; that is, of circularly polarized currents having periods of a half pendulum day. The oscillations are found to have frequency very nearly 3% higher than the local inertial frequency and vertical dependence simpler than that heretofore reported. This latter feature is held due to properties of the local stratification. It is also found to be consistent in certain respects with the motion having been generated by near-surface processes.

A brief resume is given of the work performed since 1967 by the National Institute of Oceanography in the collection of current meter records by the use of deep sea moorings and recording current meters. These records are, unlike most other current observations, accompanied by simultaneous observations of water temperature. It is possible from a knowledge of the vertical profile of temperature at or near to a mooring to derive from the temperature observations a time series which approximates to that of the vertical movement of the water. The object of this paper is to investigate the validity of equating the derived time series to that of the true vertical water motion. The spectra of potential energy of vertical motion derived from the temperature records are compared with the simultaneous spectra of horizontal kinetic energy derived from the measurements of horizontal velocities. It is concluded that under circumstances in which there are well-defined vertical gradients of temperature and density the derivation of vertical motion from a temperature record is valid and can be used with a good degree of confidence to investigate the frequency distribution of potential energy in the inertial subrange (extending from the local inertial frequency to the Brunt-Vaisala stability frequency). An idealized observational scheme is suggested which would in most cases fulfil the necessary requirements for a simple monitoring of vertical motions over long periods of time.

Statistical estimates of wind shear in the planetary boundary layer are important in the design of V/STOL aircraft, and for the design of the Space Shuttle. The data analyzed in this study consist of eleven sets of longitudinal turbulent velocity fluctuation time histories digitized at 0.2 sec intervals with approximately 18,000 data points per time history. The longitudinal velocity fluctuations were calculated with horizontal wind and direction data collected at the 18-, 30-, 60-, 90-, 120-, and 150-m levels. The data obtained confirm the result that Eulerian time spectra transformed to wave-number spectra with Taylor's frozen eddy hypothesis possess inertial-like behavior at wave-numbers well out of the inertial subrange.

The error equations for a space-stable inertial navigation system are derived. This is done by directly perturbing the mechanization equations in the inertial frame and then transforming in open-loop fashion to the local-level frame. A rotating inertial platform and velocity and altitude damping are considered. The relations between errors in space-stable and local-level systems are noted. Numerical results are presented for certain random error sources.

An extensive cruise error analysis is presented for a strapdown inertial aircraft navigation system with pulse torqued instruments, in the presence of small amplitude oscillations. The analysis accounts for complex lateral and angular vibration with realistic models of coupled motion. Steady and secularly increasing position uncertainties, with accompanying Schuler oscillations, are expressed directly in terms of familiar system constants and statistical motion parameters.

An outline is given of a preliminary attempt to apply the methods which have proved serviceable in the treatment of small-scale turbulence to the wider problem of large-scale turbulence in the atmosphere. In particular, application is made of theoretical results giving the form of the correlation function for velocity fluctuations in the inertial range according to the theory of Kolmogoroff. It appears that some of these results may be valid over a considerably greater range of eddy sizes than might at first have been anticipated. Some attempt is also made to apply these methods to the determination of the cprrelation functions for larger-scale fluctuations of pressure and temperature in the atmosphere. Actual data taken at the earth's surface and in the free atmosphere are used to test the validity of these deductions.

This paper is addressed to some aspects of low-speed inertial system alignment. Particular attention is paid to practical problems encountered which limit the accuracy of alignment. The system under study has been taken to be of the three-gimbal north-vertical configuration (#-axis vertical, #-axis north, and y-axis east), including appropriate damping and gyrocompassing means. The earth is assumed spherical. Errors in indication of the vertical and azimuth due to both component random errors and vehicle motion are treated. It is noted that, in the analysis of system response due to vehicle motions, sinusoidal test excitations although analytically convenient are not generally a valid description of the true base motions of the vehicle. In fact, it is demonstrated that such sinusoidal testing leads to overly optimistic expectation of system errors. Vehicle motions instead are described in terms of an acceleration spectral density that is peaked at some nonzero angular frequency and that contains no energy at zero frequency. This represents an attempt to account for vehicle motion more realistically. It is graphically demonstrated that, since the inertial system behaves as a low-pass filter to the hypothesized acceleration random process, longer system settling times lead to lower rms navigation errors.

Boundary and shear layers parallel to the axis of rotation in a rapidly rotating fluid are modified by inertial effects when the Rossby number R is not small enough to be neglected. If E is the Ekman number, inertial modifications to Stewartson E ¼ layers become important when the Rossby number is comparable with, or larger than, E ¼ and changes in the thickness and the structure of the layer then occur. The nature of the change depends on whether the total component of vorticity parallel to the axis of rotation is increased or diminished by the contribution from the layer. When inertial effects are important in these layers, the Ekman layers are also modified by inertia and a nonlinear Ekman condition must be used. Such a condition is obtained and it is used to discuss the flow between rotating disks when there is a discontinuity in their angular velocity and source-sink flow in an annulus.

A universal turbulence standardization technique is described which is based quantitatively on the atmospheric turbulence itself rather than on the effects it products on an aircraft. It provides a single turbulence intensity number which may be measured continuously in flight in a variety of ways, and, with knowledge of the aircraft type and speed, can be linearly related to the rms value of vertical accelerations of the aircraft. The universal intensity number concept as applied here is an extension for aircraft use of the inertial subrange concept of atmospheric turbulence. In the inertial subrange all the statistical properties of turbulence of wavelengths less than a few hundred meters (the wavelength range which dominates gust loading for most aircraft) can be simply related to a single number. The intensity measurement also has value as a basic meteorological parameter, and has proven to be particularly useful in diffusion studies. The intensity scale is derived from various turbulence pow...

The vertical displacements associated with oscillations near the local inertial frequency f, in a stratified ocean, are found to be significant, even very close to f. For a frequency omega = (1+epsilon)f, the ratio of rms vertical velocity to horizontal velocity is o(the square root of epsilon). Observations near Hawaii, made with a recently developed pycnocline follower, show inertial oscillation events similar to those found by Webster in current meter records, and discussed theoretically by Crepon, and by Pollard. (Author)

An unsteady 3D surface panel method has been developed to predict hydrodynamic load fluctuations on an ice class propeller induced by continuous variation of proximity to an ice block. The low order, time domain, combined doublet and source panel method approximates the doublet and source distribution uniformly over each panel on the propeller blades. For non-lifting bodies, i.e., the hub and ice block, only sources are distributed over the body surfaces. The simulation model is contrived in such a manner that the ice block and surrounding fluid remain stationary; and at each time step, the propeller rotates and advances forward in the inertial reference frame. This numerical model is validated with previous fixed-proximity experimental measurements and good agreement is obtained. Prediction of the fluctuating hydrodynamic load is carried out as a full dynamic interaction between the ice block and the propeller. Results for this study are compared with previous fixed-proximity numerical models and experiments. The new dynamic model establishes a basis for analysis of a more realistic fluid-structure interaction, which could, in the future, include ice block acceleration due to suction force and ice block impact loading on the propeller blade and shaft. Keywords: Marine Propulsion, Panel Methods, Unsteady Loading, Ice-Propeller Interaction doi: 10.3329/jname.v2i1.2026 Journal of Naval Architecture and Marine Engineering 2(1)(2005) 15-20

The demonstration that slow transport of clocks can be used to define simultaneity in inertial frames of reference leads to the question of whether clock transport can similarly be used in noninertial frames. It is shown that there are certain types of reference frames in which the clock-transport method cannot be used in a self-consistent manner. It is also shown that there are other types of noninertial frames in which the clock-transport method will succeed. The discussion includes noninertial frames in flat space-time as well as the case of curved space-times.

Einstein's 1911 twin-rod thought experiment is analyzed, and some of its implications for the physical status of length-contraction within the special theory of relativity are examined. Contrary to a widespread view, it is shown that the twin-rod thought experiment does not require that the two rods be travelling at equal speeds (with respect to a given inertial frame K) in order that the experiment serve its intended purpose. Since the equality or inequality of the speeds of the rods will depend upon the criterion of simultaneity adopted within the inertial frames of the special theory, the irrelevance of the speeds of the rods here indicates the synchrony-independence of this length-contraction effect within special relativity.

The transformation of the Hamiltonian of a charged particle from an inertial frame to a rotating frame in the presence of external electromagnetic fields is discussed.

In Aristotle's physics, any motion of a heavy body was either natural (toward the earth's center) or forced (away from the center). Every forced motion was required to have an external mover. For projectiles, the medium was invoked as mover. These rules precluded a true science of dynamics. Galileo, following some earlier critics, noted that rotatory motion of homogeneous spheres would be neither natural nor forced under Aristotle's definition. Investigating such “neutral” motions, he saw that they would include the motion of a heavy body over a frictionless surface concentric with the earth. Hence, motion once imparted to a body on a horizontal plane would be perpetual, and Galileo declared that a heavy body is indifferent to motion or rest in the horizontal plane and would forever remain in whichever state it was given. This restricted principle of inertia enabled Galileo and his followers to found the science of dynamics, by which physics was immeasurably advanced, though he neglected to state explicitly the general inertial principle as formulated two years after his death by Pierre Gassendi and Rene Descartes.

A theory is presented predicting the thickness of the liquid film that remains on a sheet being withdrawn from a bath under conditions that inertial forces are important. Inertial forces have been neglected in other withdrawal theories. The liquid flux does not differ much from the flux in withdrawal without inertial and capillary forces. However, the flow in the meniscus region is modified considerably. The region of applicability of this theory is compared with that of the other two withdrawal theories, for high and low C a-number withdrawal.

The fluctuations of a magnetic field in acoustic turbulence are examined. An equation is derived for the spectral tensor of homogeneous magnetic field fluctuations. In a certain limit case the spectrum of steady-state pulsations is obtained in the presence of an external source. It is shown that three kinds of spectra exist in an inertial subdomain, each of which corresponds to a definite domain in wave space. Analogous results have been obtained for the fluctuations of a homogeneous scalar impurity.

A method is developed for analyzing complex structural systems that can be divided into interconnected components. Displacements of the separate components are expressed in generalized coordinates that are defined by displacement modes. These are generated in three categories: rigid-body, "constraint," and "normal" modes. Rigid-body modes are convenient where displacements are denned in inertial space for dynamic analysis. "Constraint" modes are included to treat redundancies in the interconnection system. "Normal" modes define displacements relative to the connections. Generalized mass, stiffness, and damping matrices are determined for each component, as are generalized forces. The requirement of system continuity gives rise to equations of displacement compatibility at the connections. These serve as equations of constraint among the component coordinates and are used to construct a transformation relating component coordinates to system coordinates. This transformation is used to derive system properties and forces from component properties and forces. System equations of motion are formulated and solved to determine system response. Component responses are found using the transformation. Connection forces are computed from the component equations. Each component can then be isolated and treated separately.

Turbulence measurements obtained from concurrent tower and aircraft observations are analyzed to test G.I. Taylor's hypothesis (1938) of the equivalence between Eulerian space and Eulerian time spectra. The correlation and spectral data (along with data obtained from three other airplane turbulence programs) were also examined to ascertain the validity of Kolmogoroff's prediction (1940) for the behavior of the correlation coefficients and spectral densities in the inertial subrange. At heights of 300–400 ft above the ground, the tower and aircraft observations provide the same turbulence spectrum for wavelengths at least as large as 600 and 900 ft, for mean wind speeds of about 20 and 30 ft sec−1, respectively. The evidence is that the Kolmogoroff range is not approached for the wavelength range examined in this paper. The shortest wavelength sampled is on the order of 88 ft, at heights above the ground ranging from 200 to 2000 ft. It appears that at these heights, the Kolmogoroff spectrum, if va...

Approximate formulas, derived by use of Gora's asymptotic method, are given for rigid asymmetric rotor eigenvalues in the regions where they are degenerate in either K a or K c . The formulas are used to describe the various ways in which a resolved (or resolvable) rotational fine structure in the electronic spectra of larger molecules can arise. The formation of fine structures in the spectra of planar or near-planar molecules (such that the inertial defect, Δ, is much less than I C ) is examined in detail.

Before an inertial navigation system is used, an initialization procedure is required. The initialization procedure consists of alignment of the platform and the entry of position and velocity. A new method for the alignment of inertial navigation systems is presented in this paper. Alignment of the platform is usually accomplished by a procedure known as gyrocompassing. When gyrocompassing is employed, the inertial system is operated in a damped mode and relatively little base motion is tolerated. The well-known Kalman filter algorithm can also be used in a real time computer to align inertial navigation systems. The method discussed in this paper is in some respects similar to the Kalman filter; however, the definition of a co variance matrix is not required. Like the Kalman filter, the technique can be used to align damped and undamped inertial systems. It can be used to align inertial systems on moving or stationary vehicles. It can also be used to compute gyro drift biases in addition to platform misalignment angles. Computer simulations relating to a number of initial conditions and unmodeled error sources are discussed. It is shown that the algorithm can be used to align a system with considerable base motion.

This paper discusses an approach to linear estimation through use of a "control" fed back into the system to cancel out the effect of disturbances or error signals. Although this approach has very restricted application, it has found important usage in integrated navigation systems where one subsystem is an inertial measurement system. This approach is shown to be suboptimal and is compared with the optimal with respect to estimation accuracy and sensitivity to modeling errors. The feedback approach to estimation is shown to be similar to error estimation and correction in which the error states of the system are estimated and external correction applied. For discrete estimation using the feedback approach it is shown that error variance and Kalman gains for one-stage prediction should be used. Two examples are considered which compare the feedback approach to the optimum estimation approach. The system of the first example is quite simple, but provides simple analytical comparisons of the two estimation approaches. The second example system consists of a single-axis inertial guidance system and an independent position measuring system. Accuracy and sensitivity to modeling errors are compared. Other advantages and disadvantages of the two estimation approaches are discussed.