Partitioning the Parameter Space According to Different Behaviors During Three-Dimensional Impacts

1995 ◽  
Vol 62 (3) ◽  
pp. 740-746 ◽  
Author(s):  
V. Bhatt ◽  
J. Koechling

The equations of motion that define three-dimensional rigid-body impact with finite friction and restitution cannot be solved in a closed form. Previous work has shown that for general shapes and initial conditions, the direction of sliding velocity keeps changing continuously throughout the duration of impact. The flow patterns defined by the trace of the sliding velocity can be classified into a finite number of qualitatively distinct physical behavior. We identify three dimensionless parameters that completely specify the sliding behavior, and determine regions in this parameter space that correspond to each of the different flow patterns. The qualitative behavior during impact can now be determined based on the region which contains the parameters for a given impact configuration. The analysis is also used to study the sensitivity of the sliding behavior to changes in shape or configuration of the body and to rule out the occurrence of certain ambiguities in the post-sticking behavior during impact.

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
J.-P. Bruneton ◽  
M. Rinaldi ◽  
A. Kanfon ◽  
A. Hees ◽  
S. Schlögel ◽  
...  

Scalar-tensor theories of gravitation attract again a great interest since the discovery of the Chameleon mechanism and of the Galileon models. The former allows reconciling the presence of a scalar field with the constraints from Solar System experiments. The latter leads to inflationary models that do not need ad hoc potentials. Further generalizations lead to a tensor-scalar theory, dubbed the “Fab Four,” with only first and second order derivatives of the fields in the equations of motion that self-tune to a vanishing cosmological constant. This model needs to be confronted with experimental data in order to constrain its large parameter space. We present some results regarding a subset of this theory named “John,” which corresponds to a nonminimal derivative coupling between the scalar field and the Einstein tensor in the action. We show that this coupling gives rise to an inflationary model with very unnatural initial conditions. Thus, we include the term named “George,” namely, a nonminimal, but nonderivative, coupling between the scalar field and Ricci scalar. We find a more natural inflationary model, and, by performing a post-Newtonian analysis, we derive the set of equations that constrain the parameter space with data from experiments in the Solar System.


Some years ago it was pointed out by Prof. Proudman that all slow steady motions of a rotating liquid must be two-dimensional. If the motion is produced by moving a cylindrical object slowly through the liquid in such a way that its axis remains parallel to the axis of rotation, or if a two-dimensional motion is conceived as already existing, it seems clear that it will remain two-dimensional. If a slow three-dimensional motion is produced, then it cannot be a steady one. On the other hand, if an attempt is made to produce a slow steady motion by moving a three-dimensional body with a small uniform velocity (relative to axes which rotate with the fluid) three possibilities present themselves:— ( a ) The motion in the liquid may never become steady, however long the body goes on moving. ( b ) The motion may be steady but it may not be small in the neighbourhood of the body. ( c ) The motion may be steady and two-dimensional. In considering these three possibilities it seems very unlikely that ( a ) will be the true one. In an infinite rotating fluid the disturbance produced by starting the motion of the body might go on spreading out for ever and steady motion might never be attained, but if the body were moved steadily in a direction at right angles to the axis of rotation, and if the fluid were contained between parallel planes also perpendicular to the axis of rotation, it seems very improbable that no steady motion satisfying the equations of motion could be attained. There is more chance that ( b ) may be true. A class of mathematical expressions representing the steady motion of a sphere along the axis of a rotating liquid has been obtained. This solution of the problem breaks down when the velocity of the sphere becomes indefinitely small, in the sense that it represents a motion which does not decrease as the velocity of the sphere decreases. It seems unlikely that such a motion would be produced under experimental conditions.


1977 ◽  
Vol 28 (2) ◽  
pp. 142-148 ◽  
Author(s):  
G J Clapworthy

SummaryThe numerical calculation of the subcritical, steady, three-dimensional, potential flow past a semi-infinite swept elliptic cylinder attached to a plane wall is described. The full equations of motion are written in terms of the velocity potential and the exact body-surface conditions are applied. The equations are expressed in coordinates defined by the body shape and further transformations are necessary to reduce the infinite domain to a finite working space and to concentrate the grid points in regions of greatest variation of potential. The resulting equations are solved using a finite-difference scheme. The Mach number distribution for a typical case is presented.


Author(s):  
John Wiechel ◽  
Sandra Metzler ◽  
Dawn Freyder ◽  
Nick Kloppenborg

Reconstructing the mechanics and determining the cause of a person falling from a height in the absence of witness observations or a statement from the victim can be quite challenging. Often there is little information available beyond the final resting position of the victim and the injuries they sustained. The mechanics of a fall must follow the physics of falling bodies and this physics provides an additional source of information about how the fall occurred. Computational, physics-based simulations can be utilized to model the free-fall portion of the fall kinematics and to analyze biomechanical injury mechanisms. However, an accurate determination of the overall fall kinematics, including the initial conditions and any specific contributions of the person(s) involved, must include the correct position and posture of the individual prior to the fall. Frequently this phase of the analysis includes voluntary movement on the part of the fall victim, which cannot be modeled with simulations using anthropomorphic test devices (ATDs). One approach that has been utilized in the past to overcome this limitation is to run the simulations utilizing a number of different initial conditions for the fall victim. While fall simulations allow the initial conditions of the fall to be varied, they are unable to include the active movement of the subject, and the resulting interaction with other objects in the environment immediately prior to or during the fall. Furthermore, accurate contact interactions between the fall victim and multiple objects in their environment can be difficult to model within the simulation, as they are dependent on the knowledge of material properties of these objects and the environment such as elasticity and damping. Motion capture technology, however, allows active subject movement and behaviors to be captured in a quantitative, three-dimensional manner. This information can then be utilized within the fall simulation to more accurately model the initial fall conditions. This paper presents a methodology for reconstructing fall mechanics using a combination of motion capture, human body simulation, and injury biomechanics. This methodology uses as an example a fall situation where interaction between the fall victim and specific objects in the environment, as well as voluntary movements by the fall victim immediately prior to the accident, provided information that could not be otherwise obtained. Motion capture was first used to record the possible motions of a person in the early stages of the fall. The initial position of the fall victim within the physics based simulation of the body in free fall was determined utilizing the individual body segment and joint angles from the motion capture analysis. The methodology is applied to a real world case example and compared with the actual outcome.


2020 ◽  
Author(s):  
Nicola Giuliani ◽  
Massimiliano Rossi ◽  
Giovanni Noselli ◽  
Antonio DeSimone

AbstractEuglena gracilis is a unicellular organism that swims by beating a single anterior flagellum. We study the nonplanar waveforms spanned by the flagellum during a swimming stroke, and the three-dimensional flows that they generate in the surrounding fluid.Starting from a small set of time-indexed images obtained by optical microscopy on a swimming Euglena cell, we construct a numerical interpolation of the stroke. We define an optimal interpolation (which we call synthetic stroke) by minimizing the discrepancy between experimentally measured velocities (of the swimmer) and those computed by solving numerically the equations of motion of the swimmer driven by the trial interpolated stroke. The good match we obtain between experimentally measured and numerically computed trajectories provides a first validation of our synthetic stroke.We further validate the procedure by studying the flow velocities induced in the surrounding fluid. We compare the experimentally measured flow fields with the corresponding quantities computed by solving numerically the Stokes equations for the fluid flow, in which the forcing is provided by the synthetic stroke, and find good matching.Finally, we use the synthetic stroke to derive a coarse-grained model of the flow field resolved in terms of a few dominant singularities. The far field is well approximated by a time-varying Stresslet, and we show that the average behavior of Euglena during one stroke is that of an off-axis puller. The reconstruction of the flow field closer to the swimmer body requires a more complex system of singularities. A system of two Stokeslets and one Rotlet, that can be loosely associated with the force exerted by the flagellum, the drag of the body, and a torque to guarantee rotational equilibrium, provides a good approximation.


Author(s):  
Andrzej J. Maciejewski ◽  
Maria Przybylska

In this paper, we investigate systems of several point masses moving in constant curvature two-dimensional manifolds and subjected to certain holonomic constraints. We show that in certain cases these systems can be considered as rigid bodies in Euclidean and pseudo-Euclidean three-dimensional spaces with points which can move along a curve fixed in the body. We derive the equations of motion which are Hamiltonian with respect to a certain degenerated Poisson bracket. Moreover, we have found several integrable cases of described models. For one of them, we give the necessary and sufficient conditions for the integrability. This article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’.


1996 ◽  
Vol 169 ◽  
pp. 527-528
Author(s):  
J. Anosova ◽  
K. Tanikawa ◽  
J. Colin ◽  
L. Kiseleva ◽  
P. Eggleton

In order to investigate a possible origin for stars with high peculiar velocities in the thick disc of our Galaxy, the dynamical evolution of 16 000 three-dimensional triple systems which consist of a binary with equal or comparable masses of componentsM1andM2and a low-mass third bodyM3is considered. We examine an extensive range of initial conditions with positions of the bodyM3randomly distributed around and inside the binary orbit.M3was given the initial radial velocityV0with respect to the center of inertia of the binary. The following dynamical system of units is used in this work: the unit of distance is the semi-major axis of the binary orbit, the unit of time is the period of the binary; the universal constant of gravity is unity. In these units the total mass of the close binary is 4π2.


1970 ◽  
Vol 43 (3) ◽  
pp. 465-476 ◽  
Author(s):  
S. Ghoshal ◽  
A. Ghoshal

The equations of motion and energy governing a three-dimensional fluctuating flow of an incompressible fluid in the vicinity of a stagnation point on a regular surface have been integrated analytically. The velocity of the oncoming flow relative to the body oscillates in magnitude but not in direction.It has also been shown that the analysis of Lighthill for the two-dimensional fluctuating flow may be extended to the three-dimensional flow (both chordwise and spanwise), namely for each point on the body there is a critical frequency ω0 such that for frequencies ω > ω0 the oscillations are to a close approximation ordinary ‘shear waves’, unaffected by the mean flow; the phase advance in the skin friction is then 45°. For frequencies ω < ω0 the oscillations may be closely approximated by the sum of two parts: one quasi-steady part and the other proportional to the acceleration of the oncoming stream. The phase advance in the skin friction is then tan−1 (ω/ω0).


2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
A. I. Ismail

In this paper, the motion of a disk about a fixed point under the influence of a Newtonian force field and gravity one is considered. We modify the large parameter technique which is achieved by giving the body a sufficiently small angular velocity component r0 about the fixed z-axis of the disk. The periodic solutions of motion are obtained in the neighborhood r0 tends to 0. This case of study is excluded from the previous works because of the appearance of a singular point in the denominator of the obtained solutions. Euler-Poison equations of motion are obtained with their first integrals. These equations are reduced to a quasilinear autonomous system of two degrees of freedom and one first integral. The periodic solutions for this system are obtained under the new initial conditions. Computerizing the obtained periodic solutions through a numerical technique for validation of results is done. Two types of analytical and numerical solutions in the new domain of the angular velocity are obtained. Geometric interpretations of motion are presented to show the orientation of the body at any instant of time t.


2021 ◽  
Vol 17 (4) ◽  
pp. 507-525
Author(s):  
A. S. Shaura ◽  
◽  
V. A. Tenenev ◽  
E. V. Vetchanin ◽  
◽  
...  

This paper addresses the problem of balancing an inverted pendulum on an omnidirectional platform in a three-dimensional setting. Equations of motion of the platform – pendulum system in quasi-velocities are constructed. To solve the problem of balancing the pendulum by controlling the motion of the platform, a hybrid genetic algorithm is used. The behavior of the system is investigated under different initial conditions taking into account a necessary stop of the platform or the need for continuation of the motion at the end point of the trajectory. It is shown that the solution of the problem in a two-dimensional setting is a particular case of three-dimensional balancing.


Sign in / Sign up

Export Citation Format

Share Document