THE BEHAVIOR OF ROTATING BODIES THAT EMIT GRAVITATIONAL WAVES IN GENERAL RELATIVITY

2000 ◽  
Vol 15 (17) ◽  
pp. 1107-1115
Author(s):  
F. I. COOPERSTOCK

Recently we demonstrated that Eddington's spinning rod lost "kinetic" energy but preserved its total energy while emitting gravitational waves. Additional information is now determined by analyzing the angular momentum of the rod. We develop an expression for the angular momentum loss of the material system alone with an integration over the source region. As expected, it is found that the moment of inertia of the rod increases as the rotation rate diminishes in analogy with typical classical systems. Its rate of change is determined in relation to the angular deceleration of the body.

1973 ◽  
Vol 74 (2) ◽  
pp. 365-367 ◽  
Author(s):  
P. C. Chatwin

In a Newtonian fluid, in which the body forces are conservative, in which the pressure is a function only of density and in which the kinematic viscosity v is uniform, the vorticity ω satisfies the equationwhere u is the velocity field, so that ω = ▿ × u. This equation is normally derived by taking the curl of the Navier–Stokes equations. However, the vorticity has many interpretations in terms of the angular velocity of elements of fluid and it is natural to expect that (1) can be derived by equating the rate of change of the angular momentum of a small material volume element about its centre of mass with the moment of the forces acting on the element. Such a derivation is presented here in the hope that it may be of pedagogic interest.


1986 ◽  
Vol 114 ◽  
pp. 35-40 ◽  
Author(s):  
T. Fukushima

The definition of the angular momentum of a finite body is given in the post-Newtonian framework. The non-rotating and the rigidly rotating proper reference frame(PRF)s attached to the body are introduced as the basic coordinate systems. The rigid body in the post-Newtonian framework is defined as the body resting in a rigidly rotating PRF of the body. The feasibility of this rigidity is assured by assuming suitable functional forms of the density and the stress tensor of the body. The evaluation of the time variation of the angular momentum in the above two coordinate systems leads to the post-Newtonian Euler's equation of motion of a rigid body. The distinctive feature of this equation is that both the moment of inertia and the torque are functions of the angular velocity and the angular acceleration. The obtained equation is solved for a homogeneous spheroid suffering no torque. The post-Newtonian correction to the Newtonian free precession is a linear combination of the second, fourth and sixth harmonics of the precessional frequency. The relative magnitude of the correction is so small as of order of 10−23 in the case of the Earth.


Author(s):  
M Janneke Schwaner ◽  
Grace A Freymiller ◽  
Rulon W Clark ◽  
Craig P McGowan

Abstract Tails are widespread in the animal world and play important roles in locomotor tasks, such as propulsion, maneuvering, stability, and manipulation of objects. Kangaroo rats, bipedal hopping rodents, use their tail for balancing during hopping, but the role of their tail during the vertical evasive escape jumps they perform when attacked by predators has yet to be determined. Because we observed kangaroo rats swinging their tails around their bodies while airborne following escape jumps, we hypothesized that kangaroo rats use their tails to not only stabilize their bodies while airborne, but also to perform aerial re-orientations. We collected video data from free-ranging desert kangaroo rats (D. deserti) performing escape jumps in response to a simulated predator attack and analyzed the rotation of their bodies and tails in the yaw plane (about the vertical-axis). Kangaroo rat escape responses were highly variable. The magnitude of body re-orientation in yaw was independent of jump height, jump distance, and aerial time. Kangaroo rats exhibited a stepwise re-orientation while airborne, in which slower turning periods corresponded with the tail center of mass being aligned close to the vertical rotation axis of the body. To examine the effect of tail motion on body reorientation during a jump, we compared average rate of change in angular momentum. Rate of change in tail angular momentum was nearly proportional to that of the body, indicating that the tail reorients the body in the yaw plane during aerial escape leaps by kangaroo rats. Although kangaroo rats make dynamic 3D movements during their escape leaps, our data suggests that kangaroo rats use their tails to control orientation in the yaw plane. Additionally, we show that kangaroo rats rarely use their tail length at full potential in yaw, suggesting the importance of tail movement through multiple planes simultaneously.


2021 ◽  
Author(s):  
Leila Alizadehsaravi ◽  
Sjoerd M. Bruijn ◽  
Jaap H. van Dieen

Recovering balance after perturbations becomes challenging with aging, but an effective balance training could reduce such challenges. In this study, we examined the effect of balance training on feedback control after unpredictable perturbations by investigating balance performance, recovery strategy, and muscle synergies. We assessed the effect of balance training on unipedal perturbed balance in twenty older adults (>65 years) after short-term (one session) and long-term (3-weeks) training. Participants were exposed to random medial and lateral perturbations consisting of 8-degree rotations of a robot-controlled balance platform. We measured full-body 3D kinematics and activation of 9 muscles (8 stance leg muscles, one trunk muscle) during 2.5 s after the onset of perturbation. The perturbation was divided into 3 phases: phase1 from the onset to maximum rotation of the platform, phase 2 from the maximum rotation angle to the 0-degree angle and phase 3 after platform movement. Balance performance improved after long-term training as evidenced by decreased amplitudes of center of mass acceleration and rate of change of body angular momentum. The rate of change of angular momentum did not directly contribute to return of the center of mass within the base of support, but it reoriented the body to an aligned and vertical position. The improved performance coincided with altered activation of synergies depending on the direction and phase of the perturbation. We concluded that balance training improves control of perturbed balance, and reorganizes feedback responses, by changing temporal patterns of muscle activation. These effects were more pronounced after long-term than short-term training.


1990 ◽  
Vol 140 ◽  
pp. 27-28 ◽  
Author(s):  
A.Z. Dolginov

Difficulties of the dynamo and alternative theories of the magnetic field generation are briefly discussed. The correlation between η = lg μ/μo and ζ = lg J/Jo for rotating celestial bodies is considered. μ is the magnetic and J the angular momentum of the body. Existing theories do not explain such a correlation, and it may be an evidence for some new fundamental interaction.


Behaviour ◽  
1978 ◽  
Vol 67 (1-2) ◽  
pp. 1-65 ◽  
Author(s):  
M. 't Hart

AbstractA male stickleback with a nest but without eggs in the nest will creep through its nest fairly regularly. When a female in a glass tube is presented to the male, there is a increased chance of Creeping Through. If the female is removed after Creeping Through, the male will creep through in such way that the intervals between the Creepings Through increase in a geometric progression. If the female is not removed (and if it is impossible that she follows the male to the nest), then the intervals between the Creepings Through have the same length. If in this situation the duration of Creeping Through is shortened, either by shortening the nest, or opening the roof of the nest, or interruption of the action of Creeping Through, then the Inter Creeping Through Interval after this shortened Creeping Through, is shortened directly proportional to the shortening of the duration of Creeping Through. If the duration of Creeping Through is lengthened, either by lengthening the nest or by putting a glass-rod on the nest during Creeping Through, the length of the subsequent Inter Creeping Through Interval is not changed. There is a soll-wert for the duration of Creeping Through and the male tends towards this value even when the nest is not of normal length. In a shortened Inter Creeping Through Interval the behaviour is changed in such a way as if the first part of the normal Inter Creeping Through Interval is skipped. Because of the fact that the duration of Creeping Through is determining the length of the subsequent Inter Creeping Through Interval (if not longer than normal), we must assume that the male stickleback is able to register very precisely the duration of Creeping Through. This makes it possible to investigate which form of stimulation could be responsible for this very accurate registration. Five possible forms of exteroceptive and propioceptive stimulation which could be responsible for this registration, (and hence for the refractory period for Creeping Through) were investigated. 1. It was found that if a stimulus-situation which is more or less comparable to the stimulus-situation in the nest during Creeping Through, is presented to the male at the moment Creeping Through has to occur, this does not cause a refractory period for Creeping Through. There is only a refractory period for Creeping Through if the male creeps through a nest, but it is not necessary that the male creeps through its own nest. 2. The refractory period for Creeping Through is not caused by some form of a feedback from either reduction or accumulation during the Inter Creeping Through Interval of a secreted substance which was accumulated or reduced during Creeping Through. 3. Changing of the mechanical pressure of the nest has the effect of interrupting Creeping Through instead of affecting the rate of change of the factor which causes the refractory period for Creeping Through. 4. Tail-beating is not the proprioceptive factor which causes the refractory period for Creeping Through. A male may show less tail-beating than normal during Creeping Through but the subsequent Inter Creeping Through Interval is not shortened in proportion to the decrease of tail-beating but only in proportion to the decrease in the duration of Creeping Through. 5. The possible sensory stimulation of pharynx and/or underside of the body seems to be important in so far as it guarantees that normal Creeping Through behaviour is carried out but this stimulation is not absolutely necessary to produce a refractory period after Creeping Through. It is therefore concluded that no extero- or proprioceptive stimulation could be found which could be responsible for the registration of the duration of Creeping Through.


10.14311/664 ◽  
2005 ◽  
Vol 45 (1) ◽  
Author(s):  
O. Brůha ◽  
T. Brůha

This paper deals with an effect which appears when heating or cooling a rotating body. No external forces acting on the body are supposed. Due to thermal expansion, the moment of inertia of the body varies together with the temperature changes. In agreement with the principle of conservation of angular momentum [1], the angular momentum is constant. This results in angular velocity changes and subsequently in kinetic energy changes. Also the stress energy varies together with the changes in thermal dimension. To satisfy the principle of energy conservation we have to suppose that the changes in kinetic and stress energy are compensated by the changes in internal energy, which is correlated with temperature changes of the body. This means that the rules for the heating or cooling process of a rotating body are not the same as those for a body at rest. This idea, applied to a cylinder rotating around its geometric axis under specific parameters, has been mathematically treated. As a result, the difference between the final temperature of the rotating cylinder and the temperature of the cylinder at rest has been found. 


2017 ◽  
Vol 2017 (1) ◽  
pp. 39-54
Author(s):  
Jörg Zimmer

In classical philosophy of time, present time mainly has been considered in its fleetingness: it is transition, in the Platonic meaning of the sudden or in the Aristotelian sense of discreet moment and isolated intensity that escapes possible perception. Through the idea of subjective constitution of time, Husserl’s phenomenology tries to spread the moment. He transcends the idea of linear and empty time in modern philosophy. Phenomenological description of time experience analyses the filled character of the moment that can be detained in the performance of consciousness. As a consequence of the temporality of consciousness, he nevertheless remains in the temporal conception of presence. The phenomenology of Merleau-Ponty, however, is able to grasp the spacial meaning of presence. In his perspective of a phenomenology of perception, presence can be understood as a space surrounding the body, as a field of present things given in perception. Merleau-Ponty recovers the ancient sense of ‘praesentia’ as a fundamental concept of being in the world.


Author(s):  
DB Heyner ◽  
G Piazza ◽  
E Beeh ◽  
G Seidel ◽  
HE Friedrich ◽  
...  

A promising approach for the development of sustainable and resource-saving alternatives to conventional material solutions in vehicle structures is the use of renewable raw materials. One group of materials that has particular potential for this application is wood. The specific material properties of wood in the longitudinal fiber direction are comparable to typical construction materials such as steel or aluminum. Due to its comparatively low density, there is a very high lightweight construction potential especially for bending load cases. Structural components of the vehicle body are exposed to very high mechanical loads in the case of crash impact. Depending on the component under consideration, energy has to be absorbed and the structural integrity of the body has to be ensured in order to protect the occupants. The use of natural materials such as wood poses particular challenges for such applications. The material characteristics of wood are dispersed, and depend on environmental factors such as humidity. The aim of the following considerations was to develop a material system to ensure the functional reliability of the component. The test boundary conditions for validation also play a key role in this context. The potential of wood–steel hybrid design based on laminated veneer lumber and steel was investigated for use in a component subjected to crash loads such as the door impact beam. The chosen solution involves a separation of functions. A laminated veneer lumber-based beam was hybridized with a steel strip on the tension side. The steel strip was designed to compensate the comparatively low elongation at fracture of the wood and to ensure the integrity of the beam. The wooden component was designed for high energy absorption due to delamination and controlled failure during the impact, while maintaining the surface moment of inertia, i.e. the bending stiffness of the entire component. This approach was chosen to ensure the functional safety of the component, avoid sudden component failure and utilize the high potential of both materials. The tests carried out provided initial functional proof of the chosen solution. The hybridization achieved significantly higher deformations without sudden failure of the beam. In addition, bending capabilities were increased significantly compared to a beam without hybridization. In comparison with a state-of-the-art steel beam, the hybrid beam was not able to achieve the maximum deformation and the target weight of the hybrid beam. Further optimization of the hybrid beam is therefore necessary.


2018 ◽  
Vol 613 ◽  
pp. A66
Author(s):  
G. Fontaine ◽  
M. Latour

We show that the recent realization that isolated post-extreme horizontal branch (post-EHB) stars are generally characterized by rotational broadening with values of V rot sini between 25 and 30 km s−1 can be explained as a natural consequence of the conservation of angular momentum from the previous He-core burning phase on the EHB. The progenitors of these evolved objects, the EHB stars, are known to be slow rotators with an average value of V rot sini of ~7.7 km s−1. This implies significant spin-up between the EHB and post-EHB phases. Using representative evolutionary models of hot subdwarf stars, we demonstrate that angular momentum conservation in uniformly rotating structures (rigid-body rotation) boosts that value of the projected equatorial rotation speed by a factor ~3.6 by the time the model has reached the region of the surface gravity-effective temperature plane where the newly-studied post-EHB objects are found. This is exactly what is needed to account for their observed atmospheric broadening. We note that the decrease of the moment of inertia causing the spin-up is mostly due to the redistribution of matter that produces more centrally-condensed structures in the post-EHB phase of evolution, not to the decrease of the radius per se.


Sign in / Sign up

Export Citation Format

Share Document