scholarly journals Libration Points Inside a Spherical Cavity of a Uniformly Rotating Gravitating Ball

2021 ◽  
Vol 17 (4) ◽  
pp. 413-427
Author(s):  
A. A. Burov ◽  
◽  
V. I. Nikonov ◽  
Keyword(s):  
Spherical Cavity ◽  
Center Of Mass ◽  
Relative Equilibria ◽  
The Body ◽  
Libration Points ◽  
Homogeneous Ball ◽  
Existence And Stability ◽  
Axis Of Symmetry ◽  
Stability And Bifurcations

The problem of the existence and stability of relative equilibria (libration points) of a uniformly rotating gravitating body, which is a homogeneous ball with a spherical cavity, is considered. It is assumed that the rotation is carried out around an axis perpendicular to the axis of symmetry of the body and passing through its center of mass. The libration points located inside the cavity are investigated. Families of both isolated and nonisolated relative equilibria are found. Their stability and bifurcations are investigated. Realms of possible motion are constructed.

On the motion of bodies based on changes in the kinetic moment

2019 ◽  
Vol 20 (4) ◽  
pp. 267-275
Author(s):  
Yury N. Razoumny ◽  
Sergei A. Kupreev
Keyword(s):  
Center Of Mass ◽  
Stellar Dynamics ◽  
Elementary Particles ◽  
The Body ◽  
Accelerated Motion ◽  
Indirect Confirmation ◽  
Physical Principles ◽  
Two Bodies ◽  
Central Gravitational Field ◽  
Kinetic Moment

The controlled motion of a body in a central gravitational field without mass flow is considered. The possibility of moving the body in the radial direction from the center of attraction due to changes in the kinetic moment relative to the center of mass of the body is shown. A scheme for moving the body using a system of flywheels located in the same plane in near-circular orbits with different heights is proposed. The use of the spin of elementary particles is considered as flywheels. It is proved that using the spin of elementary particles with a Compton wavelength exceeding the distance to the attracting center is energetically more profitable than using the momentum of these particles to move the body. The calculation of motion using hypothetical particles (gravitons) is presented. A hypothesis has been put forward about the radiation of bodies during accelerated motion, which finds indirect confirmation in stellar dynamics and in an experiment with the fall of two bodies in a vacuum. The results can be used in experiments to search for elementary particles with low energy, explain cosmic phenomena and to develop transport objects on new physical principles.

scholarly journals Effect of foot–floor friction on the external moment about the body center of mass during shuffling gait: a pilot study

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Takeshi Yamaguchi ◽  
Kei Shibata ◽  
Hiromi Wada ◽  
Hiroshi Kakehi ◽  
Kazuo Hokkirigawa
Keyword(s):  
Friction Surface ◽  
Center Of Mass ◽  
Young Male ◽  
The Body ◽  
Low Friction ◽  
Surface Conditions ◽  
Normal Gait ◽  
External Moment ◽  
Body Center ◽  
Floor Condition

AbstractHerein, we investigated the effect of friction between foot sole and floor on the external forward moment about the body center of mass (COM) in normal and shuffling gaits. Five young male adults walked with normal and shuffling gaits, under low- and high-friction surface conditions. The maximum external forward moment about the COM (MEFM-COM) in a normal gait appeared approximately at initial foot contact and was unaffected by floor condition. However, MEFM-COM in a shuffling gait under high-friction conditions exceeded that under low-friction conditions (p < 0.001). Therein, MEFM-COM increased with an increasing utilized coefficient of friction at initial foot contact; this effect was weaker during a normal gait. These findings indicate that increased friction between foot sole and floor might increase tripping risk during a shuffling gait, even in the absence of discrete physical obstacles.

scholarly journals Can Muscle Stiffness Alone Stabilize Upright Standing?

1999 ◽  
Vol 82 (3) ◽  
pp. 1622-1626 ◽  
Author(s):  
Pietro G. Morasso ◽  
Marco Schieppati
Keyword(s):  
Center Of Pressure ◽  
Center Of Mass ◽  
Muscle Stiffness ◽  
The Body ◽  
Ankle Muscles ◽  
Upright Standing ◽  
Stiffness Control ◽  
Control Patterns ◽  
Physiological Values

A stiffness control model for the stabilization of sway has been proposed recently. This paper discusses two inadequacies of the model: modeling and empiric consistency. First, we show that the in-phase relation between the trajectories of the center of pressure and the center of mass is determined by physics, not by control patterns. Second, we show that physiological values of stiffness of the ankle muscles are insufficient to stabilize the body “inverted pendulum.” The evidence of active mechanisms of sway stabilization is reviewed, pointing out the potentially crucial role of foot skin and muscle receptors.

On planar oscillations of a body with a variable mass distribution in an elliptic orbit

2011 ◽  
Vol 225 (10) ◽  
pp. 2288-2295 ◽  
Author(s):  
A Burov ◽  
I Kosenko
Keyword(s):  
Mass Distribution ◽  
Large Scale ◽  
Variable Mass ◽  
Relative Equilibria ◽  
The Body ◽  
Global Dynamics ◽  
Central Field ◽  
Attitude Dynamics ◽  
Orbital Eccentricity ◽  
Space Elevators

Planar motion of an orbiting body having a variable mass distribution in a central field of gravity is under analysis. Within the so-called ‘satellite approximation’ planar attitude dynamics is reduced to the 3/2-degrees of freedom description by one ODE of second order. The law of the mass distribution variations implying an existence of the special relative equilibria, such that the body is oriented pointing to the attracting centre by the same axis for any value of the orbit eccentricity is indicated. For particular example of an orbiting dumb-bell equipped by a massive cabin, wandering between the ends of the dumb-bell. For this example stability of the equilibria such that the dumb-bell ‘points to’ the attracting centre by one of its ends is studied. The chaoticity of global dynamics is investigated. Two important examples of a vibrating dumb-bell and of a dumb-bell equipped by a cabin wandering between its endpoints are considered. The dynamics of space objects, including moving elements, has been investigated by many authors. These studies usually have been connected with the necessity to estimate the influence of relative motions of moving parts, for example, crew motions [ 1 , 2 ], circulation of liquids [ 3 ], etc. on the attitude dynamics of a spacecraft. The development of projects of large-scale space systems with mobile elements, in particular, of satellite systems with tethered elements and space elevators, has posed problems related to their dynamics. Various aspects of the role of mass distribution even for the simplest orbiting systems, like dumb-bell systems are known since the publications [ 4 – 7 ], etc. The possibility of the sudden loss of stability because of the mass redistribution has been pointed out in reference [ 8 ] (see also references [ 9 – 13 ]). The considered system belongs to the mentioned class of systems and represents by itself one of the simplest systems allowing both analytical and numerical treatment, without supplementary simplifying assumptions such as smallness of the orbital eccentricity. Another set of applied problems is related to orientation keeping of the system for deployment and retrieval of tethered subsatellites as well as for relative cabin motions of space elevators. In particular, the problem of the stabilization/destabilization possibility for the given state of motion due to rapid oscillations of the cabin exists. This could be the subject of another additional investigation.

The Forced Oscillations of Submerged Bodies

2003 ◽  
Vol 125 (4) ◽  
pp. 710-715
Author(s):  
Angel Sanz-Andre´s ◽  
Gonzalo Tevar ◽  
Francisco-Javier Rivas
Keyword(s):  
Rigid Body ◽  
Small Amplitude ◽  
Center Of Mass ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Central Point ◽  
Modal Testing ◽  
Forced Oscillations ◽  
Motion Equations ◽  
Marine Applications

The increasing use of very light structures in aerospace applications are given rise to the need of taking into account the effects of the surrounding media in the motion of a structure (as for instance, in modal testing of solar panels or antennae) as it is usually performed in the motion of bodies submerged in water in marine applications. New methods are in development aiming at to determine rigid-body properties (the center of mass position and inertia properties) from the results of oscillations tests (at low frequencies during modal testing, by exciting the rigid-body modes only) by using the equations of the rigid-body dynamics. As it is shown in this paper, the effect of the surrounding media significantly modifies the oscillation dynamics in the case of light structures and therefore this effect should be taken into account in the development of the above-mentioned methods. The aim of the paper is to show that, if a central point exists for the aerodynamic forces acting on the body, the motion equations for the small amplitude rotational and translational oscillations can be expressed in a form which is a generalization of the motion equations for a body in vacuum, thus allowing to obtain a physical idea of the motion and aerodynamic effects and also significantly simplifying the calculation of the solutions and the interpretation of the results. In the formulation developed here the translational oscillations and the rotational motion around the center of mass are decoupled, as is the case for the rigid-body motion in vacuum, whereas in the classical added mass formulation the six motion equations are coupled. Also in this paper the nonsteady motion of small amplitude of a rigid body submerged in an ideal, incompressible fluid is considered in order to define the conditions for the existence of the central point in the case of a three-dimensional body. The results here presented are also of interest in marine applications.

Many-legged maneuverability: dynamics of turning in hexapods

1999 ◽  
Vol 202 (12) ◽  
pp. 1603-1623 ◽  
Author(s):  
D.L. Jindrich ◽  
R.J. Full
Keyword(s):  
Horizontal Plane ◽  
Center Of Mass ◽  
Vertical Plane ◽  
Force Production ◽  
The Body ◽  
Mean Velocity ◽  
Blaberus Discoidalis ◽  
Body Design ◽  
Reaction Forces ◽  
Straight Ahead

Remarkable similarities in the vertical plane of forward motion exist among diverse legged runners. The effect of differences in posture may be reflected instead in maneuverability occurring in the horizontal plane. The maneuver we selected was turning during rapid running by the cockroach Blaberus discoidalis, a sprawled-postured arthropod. Executing a turn successfully involves at least two requirements. The animal's mean heading (the direction of the mean velocity vector of the center of mass) must be deflected, and the animal's body must rotate to keep the body axis aligned with the heading. We used two-dimensional kinematics to estimate net forces and rotational torques, and a photoelastic technique to estimate single-leg ground-reaction forces during turning. Stride frequencies and duty factors did not differ among legs during turning. The inside legs ended their steps closer to the body than during straight-ahead running, suggesting that they contributed to turning the body. However, the inside legs did not contribute forces or torques to turning the body, but actively pushed against the turn. Legs farther from the center of rotation on the outside of the turn contributed the majority of force and torque impulse which caused the body to turn. The dynamics of turning could not be predicted from kinematic measurements alone. To interpret the single-leg forces observed during turning, we have developed a general model that relates leg force production and leg position to turning performance. The model predicts that all legs could turn the body. Front legs can contribute most effectively to turning by producing forces nearly perpendicular to the heading, whereas middle and hind legs must produce additional force parallel to the heading. The force production necessary to turn required only minor alterations in the force hexapods generate during dynamically stable, straight-ahead locomotion. A consideration of maneuverability in the horizontal plane revealed that a sprawled-postured, hexapodal body design may provide exceptional performance with simplified control.

Long bone cross-sectional geometry

2020 ◽  
pp. 307-320
Author(s):  
Christopher B. Ruff ◽  
Ryan W. Higgins ◽  
Kristian J. Carlson
Keyword(s):  
Mechanical Properties ◽  
Cross Sections ◽  
Lateral Displacement ◽  
Center Of Mass ◽  
Gait Pattern ◽  
Locomotor Behavior ◽  
The Body ◽  
Long Bone ◽  
Cross Sectional ◽  
Body Center

Long bone diaphyseal cross-sectional geometries reflect the mechanical properties of the bones, and can be used to aid in inferences of locomotor behavior in extinct hominins. This chapter considers all available long bone diaphyseal and femoral neck cross-sections of specimens from Sterkfontein Member 4, and presents comparisons of these section properties and other cross-sectional dimensions with those of other early hominins as well as modern samples. The cross-sectional geometry of the Sterkfontein Member 4 long bone specimens suggests some similarities to, but also interesting differences in, mechanical loading of these elements relative to modern humans. The less asymmetric cortical bone distribution in the Sterkfontein femoral necks is consistent with other evidence above indicating an altered gait pattern involving lateral displacement of the body center of mass over the stance limb. The relatively very strong upper limb of StW 431 implies that arboreal behavior formed a significant component of its locomotor repertoire. Bipedal gait may have been less efficient and arboreal climbing more prevalent in the Sterkfontein hominins.

scholarly journals Physiological Gait versus Gait in VR on Multidirectional Treadmill—Comparative Analysis

Medicina ◽  
2019 ◽  
Vol 55 (9) ◽  
pp. 517 ◽  
Author(s):  
Katarzyna Jochymczyk-Woźniak ◽  
Katarzyna Nowakowska ◽  
Jacek Polechoński ◽  
Sandra Sładczyk ◽  
Robert Michnik
Keyword(s):  
Comparative Analysis ◽  
Knee Joint ◽  
Hip Joint ◽  
Pelvic Tilt ◽  
Plantar Flexion ◽  
Center Of Mass ◽  
The Body ◽  
Joint Rotation ◽  
Active Motion ◽  
Flexion Extension

Background and objectives: Virtual reality (VR) is increasingly often finding applications in physiotherapy and health promotion. Recent years have seen the use of advanced technologies in the promotion of physical activity (PA) in society. New simulators, e.g., treadmills, enable the performance of PA (e.g., locomotive movements) in VR (artificially created virtual world). The question of how such movements are similar to natural forms of human locomotion (march, run) inspired the comparative analysis of physiological gait and gait in VR on a multidirectional Omni treadmill. Materials and Methods: The tests involved the use of the BTS Smart system for the triplanar analysis of motion. The test involved 10 healthy females aged 20–24 (weight: 52 ± 3.1 kg, height 162 ± 5.4 cm). Measurements were performed at two stages. The first stage involved the standard assessment of physiological gait, whereas the second was focused on gait forced by the Omni treadmill. The following gait parameters were analyzed: Flexion-extension in the ankle, knee joint and hip joint, rotation in the hip joint and knee joint, foot progression, adduction-abduction in the knee joint and hip joint, pelvic obliquity, pelvic tilt, pelvic rotation as well as energy expenditure and the movement of the body center of mass. Results: The analysis of the test results revealed the existence of differences in the kinematics of physical gait and gait on the treadmill. The greatest differences were recorded in relation to the dorsal-plantar flexion in the ankle, the foot progression, the rotation of the knee joint, pelvic tilt and rotation. In addition, the gait on the treadmill is characterized by the longer duration of the stance phase and reduced ranges of the following movements: Flexion-extension in the ankle, knee joint and hip joint, adduction-abduction in the hip joint as well as rotation in the ankle and hip joint. The values of potential, kinetic and total energy recorded in relation to forced gait are significantly lower than those of physiological gait. Conclusions: Because of the fact that the parameters of gait on the Omni platform vary significantly from the parameters of physical gait, the application of the Omni treadmill in the re-education of gait during rehabilitation should be treated with considerable care. Nonetheless, the treadmill has adequate potential to become a safe simulator enabling active motion in VR using locomotive movements.

Perturbed rotational motions of a spheroid with cavity filled with a viscous fluid

2020 ◽  
pp. 095440622094154
Author(s):  
LD Akulenko ◽  
DD Leshchenko ◽  
KS Paly
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Numerical Solution ◽  
Nonlinear Evolution ◽  
Center Of Mass ◽  
The Body ◽  
Angular Motion ◽  
Asymptotic Approach ◽  
Averaged Equations ◽  
Rotational Motions

We consider a motion about the center of mass of a spheroid with a cavity filled with a viscous fluid. It is assumed that the velocity of the fluid is sufficiently high, so the corresponding Reynolds number is small. The torque of forces acting on the body by the viscous fluid in the cavity is determined by the method developed in the works of F.L. Chernousko. Asymptotic approach permits to obtain some qualitative results and to describe nonlinear evolution of angular motion using simplified averaged equations and numerical solution.

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