scholarly journals Relaxation of viscoelastic tumblers with application to 1I/2017 (‘Oumuamua) and 4179 Toutatis

2020 ◽  
Vol 497 (1) ◽  
pp. 19-36 ◽  
Author(s):  
James A Kwiecinski
Keyword(s):  
Stress Field ◽  
General Theory ◽  
Continuum Mechanics ◽  
Time Scale ◽  
Principal Axis ◽  
Inertial Forces ◽  
Short Axis ◽  
Q Factor ◽  
Analytic Approximations ◽  
Viscoelastic Parameters

ABSTRACT Motivated by the observation of comets and asteroids rotating in non-principal axis (NPA) states, we investigate the relaxation of a freely precessing triaxial ellipsoidal rotator towards its lowest energy spin state. Relaxation of the precession arises from internal dissipative stresses generated by self-gravitation and inertial forces from spin. We develop a general theory to determine the viscoelastic stresses in the rotator, under any linear rheology, for both long-axis (LAM) and short-axis (SAM) modes. By the methods of continuum mechanics, we calculate the power dissipated by the stress field and the viscoelastic material strain, which enables us to determine the time-scale of the precession dampening. To illustrate how the theory is used, we apply our framework to a triaxial 1I/2017 (‘Oumuamua) and 4179 Toutatis under the Maxwell regime. For the former, employing viscoelastic parameters typical of very cold monolithic asteroids renders a dampening time-scale longer by a factor of 1010 and higher than the time-scales found in the works relying on the $\, Q$-factor approach, while the latter yields a time-scale shorter by 107 as a consequence of including self-gravitation. We further reduce our triaxial theory to bodies of an oblate geometry and derive a family of relatively simple analytic approximations determining the NPA dampening times for Maxwell rotators, as well as a criterion determining whether self-gravitation is negligible in the relaxation process. Our approximations exhibit a relative error no larger than $0.2{{\ \rm per\ cent}}$, when compared to numerical integration, for close to non-dissipative bodies and $0.003{{\ \rm per\ cent}}$ for moderately to highly energy dissipating rotators.

Effect of finite boundaries on the Stokes resistance of an arbitrary particle

1962 ◽  
Vol 12 (1) ◽  
pp. 35-48 ◽  
Author(s):  
Howard Brenner
Keyword(s):  
Experimental Data ◽  
General Theory ◽  
Spherical Particle ◽  
Principal Axis ◽  
Wall Effect ◽  
Wall Proximity

A general theory is put forward for the effect of wall proximity on the Stokes resistance of an arbitrary particle. The theory is developed completely for the case where the motion of the particle is parallel to a principal axis of resistance. In this case, the wall-effect correction can be calculated entirely from a knowledge of the force experienced by the particle in anunboundedfluid, providing (i) that the wall correction is already known for a spherical particle and (ii) that the particle is small in comparison to its distance from the boundary. Experimental data are cited which confirm the theory. The theory is extended to the wall effect on a particlerotatingnear a boundary.

scholarly journals Generalization of Haefeli’s Creep-Angle Analysis

1972 ◽  
Vol 11 (63) ◽  
pp. 447-450 ◽  
Author(s):  
R. I. Perla
Keyword(s):  
Partial Differential Equations ◽  
Stress Field ◽  
Differential Equations ◽  
Stress Analysis ◽  
Continuum Mechanics ◽  
Deformation Rate ◽  
Rate Coefficient ◽  
Partial Differential ◽  
Key Parameter

Abstract Using geometrical arguments, Haefeli developed a stress analysis for slabs of compressible viscous materials. His analysis was based on a key parameter called the creep angle. A generalization of the creep angle, called the deformation-rate coefficient, is derived by replacing geometrical arguments with continuum mechanics. Once the deformation-rate coefficient is found from in situ measurements, the stress field of the slab can be determined from a set of hyperboic partial differential equations.

scholarly journals Asteroid Spins: From the Very Fast to the Very Slow

1997 ◽  
Vol 165 ◽  
pp. 265-268
Author(s):  
A. W. Harris ◽  
W.Z. Wisniewski
Keyword(s):  
Solar System ◽  
Time Scale ◽  
Rotation Rate ◽  
Principal Axis ◽  
Ccd Photometry ◽  
Radar Observations ◽  
The Earth ◽  
Axis Rotation

The application of CCD photometry to monitoring the light variations of very small asteroids has led to an explosion of data available, and perhaps as importantly, has made it possible to probe fainter, and hence smaller asteroids. In this paper, we review several new results from the analysis of such lightcurve data, much of it taken by the late W. Z. Wisniewski, a native of Poland who studied at Poznan University (Wisniewski et al., 1997).At the time of the last close pass of the asteroid 4179 Toutatis by the Earth in 1992, it became apparent from radar observations that the asteroid was in a bizarre rotation state, and that the rotation rate was extremely slow. Harris (1994), re-evaluating the work by Burns and Safronov (1973) found that very small and slowly rotating asteroids can have a time scale of damping into a principal-axis rotation state which is long compared to their expected collisional lifetime, or for that matter, the age of the solar system:

scholarly journals The Theory of Optimal Balancing of Mechanisms

2019 ◽  
Vol 10 (1) ◽  
pp. 59-66
Author(s):  
István Papp ◽  
Márton Máté
Keyword(s):  
Fourier Series ◽  
General Theory ◽  
The Body ◽  
Inertial Forces ◽  
Mass Center

Abstract This paper presents a general theory regarding the balancing of mechanisms. It starts with Stevenson’s theory [1], which proves that any mechanism can be dynamically perfectly balanced if there is a pair of counterweights that are eccentrically positioned in three reciprocating perpendicular axes, passing through the mass center of the body. The system of inertial forces are extended in Fourier series where only the first terms, the basic harmonics, are considered. The proposed goal is to stultify the effect of inertial forces and torques. This paper deals with a situation more appropriate to reality. In common cases there doesn’t exist the possibility of implementing counterweights in three perpendicular axes. In this situation only the minimization of inertial forces and torques remains as a possible solution. The method developed for this case is presented.

A review of the general theory of thermoelastic stress analysis

2003 ◽  
Vol 38 (5) ◽  
pp. 405-417 ◽  
Author(s):  
G Pitarresi ◽  
E. A Patterson
Keyword(s):  
Stress Field ◽  
General Theory ◽  
Stress Analysis ◽  
Experimental Technique ◽  
Surface Stress ◽  
Thermoelastic Stress ◽  
Thermodynamic Theory ◽  
Thermoelastic Stress Analysis ◽  
Thermoelastic Effect ◽  
Insight Into

Thermoelastic stress analysis (TSA) is now a well-known experimental technique providing information on the surface stress field in structures. Many studies have assessed the potential of the technique for a number of applications and some useful and detailed reviews of these investigations are available, focusing mainly on the experimental aspects related to the measurement of the thermoelastic signal. In this work, instead, a complete and detailed insight into the origins of the various forms of the equations describing the thermoelastic effect is given with reference to the concepts of the thermodynamic theory of a continuum. A discussion on the theory leading to the thermoelastic effect law is intended to give a useful overview of the applications and real limitations of TSA.

Two-time scale controller design for a high speed planar parallel manipulator with structural flexibility

Robotica ◽  
2002 ◽  
Vol 20 (5) ◽  
pp. 519-528
Author(s):  
Bongsoo Kang ◽  
Benny Yeung ◽  
James K. Mills
Keyword(s):  
Time Scale ◽  
Parallel Manipulator ◽  
High Speed ◽  
Parallel Manipulators ◽  
Structural Vibration ◽  
Scale Model ◽  
Fast Time ◽  
Inertial Forces ◽  
Linear Quadratic ◽  
Planar Parallel Manipulator

SummaryPlanar parallel manipulators, with potential applications in high speed, high acceleration tasks such as electronic component placement, would be subject to mechanical vibration due to high inertial forces acting on the linkages and other components. To achieve high throughput capability, such motion induced vibration would have to be damped quickly, to reduce settling time of the platform position and orientation. This paper develops a two-time scale dynamic model of a three-degree-of-freedom planar parallel manipulator with structurally flexible linkages. Based on the two-time scale model, a composite controller, consisting of a computed torque controller for the slow time-scale or rigid body subsystem dynamics, and a linear-quadratic state-feedback regulator for the fast time-scale flexible dynamic subsystem, is designed. Simulation results show that the composite control scheme permits the parallel manipulator platform to follow a given desired trajectory, while damping structural vibration arising due to excitation from inertial forces.

scholarly journals Observations on stages of upwelling in the region of Cabo Frio (Brazil) as conducted by continuous surface temperature and salinity measurements

1974 ◽  
Vol 23 (0) ◽  
pp. 33-46 ◽  
Author(s):  
Y. Ikeda ◽  
L.B. de Miranda ◽  
N.J. Rock
Keyword(s):  
Stress Field ◽  
Surface Temperature ◽  
Time Scale ◽  
Rapid Change ◽  
Coastal Region ◽  
The West ◽  
Continuous Surface ◽  
Wind Stress Field ◽  
Counter Current ◽  
Cabo Frio

A brief outline is given of the results of surface temperature and salinity to the west and southwest of Cabo Frio obtained in August of 1971 with a continuous recording Thermo-Salinograph (Bissett-Berman, Model 6600T). A rapid change was observed in the field distribution of temperature from 21.5-21.9ºC to 15-21ºC, and similary change in the distribution of salinity from 34.1-35.0º/oo to 35.3-36.0º/oo, over a time scale of seven days. The changes were accredited to the process of upwelling at the coastal region under the influence of E and NE winds. The occurrence of a surface counter-current moving upwind was detected. This anomaly, not explained on the basis of the Ekman's classical theory, was qualitatively explained as the result of a horizontal divergence in the wind-stress field.

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