ENVELOPING SURFACES AND ADMISSIBLE VELOCITIES OF HEAVY RIGID BODIES

2004 ◽  
Vol 14 (08) ◽  
pp. 2525-2553 ◽  
Author(s):  
IGOR N. GASHENENKO ◽  
PETER H. RICHTER
Keyword(s):  
Three Dimensional ◽  
Rigid Bodies ◽  
First Integrals ◽  
The Body ◽  
Heegaard Splitting ◽  
Body Motion ◽  
Invariant Sets ◽  
Poisson Problem ◽  
Integral Manifolds ◽  
Angular Velocities

The general Euler-Poisson problem of rigid body motion is investigated. We study the three-dimensional algebraic level surfaces of the first integrals, and their topological bifurcations. The main result of this article is an analytical and qualitatively complete description of the projections of these integral manifolds to the body-fixed space of angular velocities. We classify the possible types of these invariant sets and analyze the dependence of their topology on the parameters of the body and the constants of the first integrals. Particular emphasis is given to the enveloping surfaces of the sets of admissible angular velocities. Their pre-images in the reduced phase space induce a Heegaard splitting which lends itself for a general choice of complete Poincaré surfaces of section, irrespective of whether or not the system is integrable.

Flight performance and visual control of flight of the free-flying housefly ( Musca domestica L.) I. Organization of the flight motor

1986 ◽  
Vol 312 (1158) ◽  
pp. 527-551 ◽  
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
The Body ◽  
Midsagittal Plane ◽  
Torque Vector ◽  
Translation Velocity ◽  
Flight Motor

Free-flying houseflies have been filmed simultaneously from two sides. The orientation of the flies’ body axes in three-dimensional space can be seen on the films. A method is presented for the reconstruction of the flies’ movements in a fly-centred coordinate system, relative to an external coordinate system and relative to the airstream. The flies are regarded as three-dimensionally rigid bodies. They move with respect to the six degrees of freedom they thus possess. The analysis of the organization of the flight motor from the kinematic data leads to the following conclusions: the sideways movements can, at least qualitatively, be explained by taking into account the sideways forces resulting from rolling the body about the long axis and the influence of inertia. Thus, the force vector generated by the flight motor is most probably located in the fly’s midsagittal plane. The direction of this vector can be varied by the fly in a restricted range only. In contrast, the direction of the torque vector can be freely adjusted by the fly. No coupling between the motor force and the torques is indicated. Changes of flight direction may be explained by changes in the orientation of the body axes: straight flight at an angle of sideslip differing from zero is due to rolling. Sideways motion during the banked turns as well as the decrease of translation velocity observed in curves are a consequence of the inertial forces and rolling. The results are discussed with reference to studies about the aerodynamic performance of insects and the constraints for aerial pursuit.

Identifying Sets of Constraint Forces by Inspection

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
Carlos M. Roithmayr ◽  
Dewey H. Hodges
Keyword(s):  
Mechanical System ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
The Body ◽  
Vector Form ◽  
Constraint Forces ◽  
Constraint Force ◽  
Symbolic Algebra ◽  
Constraint Equations ◽  
Angular Velocities

A mechanical system is often modeled as a set of particles and rigid bodies, some of which are constrained in one way or another. A concise method is proposed for identifying a set of constraint forces needed to ensure the restrictions are met. Identification consists of determining the direction of each constraint force and the point at which it must be applied, as well as the direction of the torque of each constraint force couple, together with the body on which the couple acts. This important information can be determined simply by inspecting constraint equations written in vector form. For the kinds of constraints commonly encountered, the constraint equations are expressed in terms of dot products involving velocities of the affected points or particles and angular velocities of the bodies concerned. The technique of expressing constraint equations in vector form and identifying constraint forces by inspection is useful when one is deriving explicit, analytical equations of motion by hand or with the aid of symbolic algebra software, as demonstrated with several examples.

Oscillatory motion and wake instability of freely rising axisymmetric bodies

2007 ◽  
Vol 573 ◽  
pp. 479-502 ◽  
Author(s):  
PEDRO C. FERNANDES ◽  
FRÉDÉRIC RISSO ◽  
PATRICIA ERN ◽  
JACQUES MAGNAUDET
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Axial Velocity ◽  
Body Shape ◽  
Rigid Bodies ◽  
The Body ◽  
Body Motion ◽  
Wake Instability ◽  
Moving Bodies

This paper reports on an experimental study of the motion of freely rising axisym- metric rigid bodies in a low-viscosity fluid. We consider flat cylinders with height h smaller than the diameter d and density ρb close to the density ρf of the fluid. We have investigated the role of the Reynolds number based on the mean rise velocity um in the range 80 ≤ Re = umd/ν ≤ 330 and that of the aspect ratio in the range 1.5 ≤ χ = d/h ≤ 20. Beyond a critical Reynolds number, Rec, which depends on the aspect ratio, both the body velocity and the orientation start to oscillate periodically. The body motion is observed to be essentially two-dimensional. Its description is particularly simple in the coordinate system rotating with the body and having its origin fixed in the laboratory; the axial velocity is then found to be constant whereas the rotation and the lateral velocity are described well by two harmonic functions of time having the same angular frequency, ω. In parallel, direct numerical simulations of the flow around fixed bodies were carried out. They allowed us to determine (i) the threshold, Recf1(χ), of the primary regular bifurcation that causes the breaking of the axial symmetry of the wake as well as (ii) the threshold, Recf2(χ), and frequency, ωf, of the secondary Hopf bifurcation leading to wake oscillations. As χ increases, i.e. the body becomes thinner, the critical Reynolds numbers, Recf1 and Recf2, decrease. Introducing a Reynolds number Re* based on the velocity in the recirculating wake makes it possible to obtain thresholds $\hbox{\it Re}^*_{cf1}$ and $\hbox{\it Re}^*_{cf2}$ that are independent of χ. Comparison with fixed bodies allowed us to clarify the role of the body shape. The oscillations of thick moving bodies (χ < 6) are essentially triggered by the wake instability observed for a fixed body: Rec(χ) is equal to Recf1(χ) and ω is close to ωf. However, in the range 6 ≤ χ ≤ 10 the flow corrections induced by the translation and rotation of freely moving bodies are found to be able to delay the onset of wake oscillations, causing Rec to increase strongly with χ. An analysis of the evolution of the parameters characterizing the motion in the rotating frame reveals that the constant axial velocity scales with the gravitational velocity based on the body thickness, $\sqrt{((\rho_f-\rho_b)/\rho_f)\,gh}$, while the relevant length and velocity scales for the oscillations are the body diameter d and the gravitational velocity based on d, $\sqrt{((\rho_f-\rho_b)/\rho_f)\,gd}$, respectively. Using this scaling, the dimensionless amplitudes and frequency of the body's oscillations are found to depend only on the modified Reynolds number, Re*; they no longer depend on the body shape.

scholarly journals Cases of Integrability Which Correspond to the Motion of a Pendulum in the Three-dimensional Space

2021 ◽  
Vol 16 ◽  
pp. 73-84
Author(s):  
Maxim V. Shamolin
Keyword(s):  
Rigid Body ◽  
Force Fields ◽  
Characteristic Point ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
The Body ◽  
Spatial Motion ◽  
Free Rigid Body

We systematize some results on the study of the equations of spatial motion of dynamically symmetric fixed rigid bodies–pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of a spatial motion of a free rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint, or the center of mass of the body moves rectilinearly and uniformly; this means that there exists a nonconservative couple of forces in the system

scholarly journals Dynamics of constrained many body problems in constant curvature two-dimensional manifolds

2018 ◽  
Vol 376 (2131) ◽  
pp. 20170425 ◽  
Author(s):  
Andrzej J. Maciejewski ◽  
Maria Przybylska
Keyword(s):  
Constant Curvature ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Rigid Bodies ◽  
The Body ◽  
Two Dimensional ◽  
Many Body ◽  
Finite Dimensional ◽  
Necessary And Sufficient

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’.

Hydrodynamics of larval fish quick turning: A computational study

2017 ◽  
Vol 232 (14) ◽  
pp. 2515-2523 ◽  
Author(s):  
Jialei Song ◽  
Yong Zhong ◽  
Haoxiang Luo ◽  
Yang Ding ◽  
Ruxu Du
Keyword(s):  
Larval Fish ◽  
Computational Study ◽  
Three Dimensional ◽  
Interaction Model ◽  
The Body ◽  
Body Motion ◽  
Body Interaction ◽  
Fluid Body ◽  
Preparatory Stage ◽  
Tangential Acceleration

A three-dimensional fluid–body interaction model was established to study the hydrodynamics of larval fish at a quick start with a turning angle of approximately 80°. The bending curves of the larval fish were attained by extracting the middle line of fish snapshots from a previously published paper. The fluid–body interaction was implemented to empower the self-propelling function of the larval fish. In this study, the swimmer’s kinematics of the body as well as hydrodynamics at preparatory and propulsive stages of the larval fish were extensively analysed. It shows that during the preparatory stage, the larval fish produces a significant force against the escaping direction. Nevertheless, this force leads to a large turning torque, helping to accomplish a quick turning. During the propulsive stage, the force increases quickly in the escape direction, resulting in a large velocity for the escape. The characteristics of body motion and the flow field are consistent with the previous observation on adult fish: the bimodal mode on velocity and tangential acceleration and three jets of fluids. In addition, the research also reveals that the forces generated at anterior and posterior parts of the larval fish generally point to the opposite directions at both preparatory and propulsive strokes of C-start.

On the coupled time-harmonic motion of water and a body freely floating in it

2011 ◽  
Vol 679 ◽  
pp. 616-627 ◽  
Author(s):  
NIKOLAY KUZNETSOV ◽  
OLEG MOTYGIN
Keyword(s):  
Boundary Value Problem ◽  
Small Amplitude ◽  
Three Dimensional ◽  
Water Layer ◽  
The Body ◽  
Body Motion ◽  
Constant Depth ◽  
Harmonic Motion ◽  
Time Harmonic ◽  
Equipartition Of Energy

We consider a spectral problem that describes the time-harmonic small-amplitude motion of the mechanical system that consists of a three-dimensional water layer of constant depth and a body (either surface-piercing or totally submerged), freely floating in it. This coupled boundary-value problem contains a spectral parameter – the frequency of oscillations – in the boundary conditions as well as in the equations governing the body motion. It is proved that the total energy of the water motion is finite and the equipartition of energy of the whole system is established. Under certain restrictions on body's geometry the problem is proved to have only a trivial solution for sufficiently large values of the frequency. The uniqueness frequencies are estimated from below.

An Approach Experimentally Based Modeling and Simulation of Human Motion

2008 ◽  
Author(s):  
Jenchieh Lee ◽  
Henryk Flashner ◽  
Jill McNitt-Gray
Keyword(s):  
Dynamic Properties ◽  
Three Dimensional ◽  
Optimal Solution ◽  
Iteration Process ◽  
Momentum Conservation ◽  
Human Motion ◽  
Rigid Bodies ◽  
Body Motion ◽  
Penalty Function Method ◽  
Three Dimension

A computational approach for estimating three-dimensional human body motion from measurement of marker locations during motion is proposed. The proposed method computes the system’s kinematics while preserving important physical and dynamic properties. These properties include preserving the connection point (joint) between any two neighboring bodies and satisfying total body linear and angular momentum conservation laws. Four sets of equations are formulated for kinematic and dynamic properties of body segments. Attitude estimation is based on Wahba’s problem [1], and dynamic and kinematic constraints are included by utilizing penalty function method. An iteration process is presented to combine the four sets of estimation measure to ensure convergence to the optimal solution. Two examples are presented to demonstrate the performance of the proposed method: estimation of the kinematics of a chain of rigid bodies obtained by computer simulation, and estimation of motion in three dimension of a diver obtained using experimental measurements. The results of both examples show fast convergence of the algorithm to an optimal solution while satisfying the imposed the constraints.

scholarly journals Water entry of a body which moves in more than six degrees of freedom

2015 ◽  
Vol 471 (2177) ◽  
pp. 20150058 ◽  
Author(s):  
Y.-M. Scolan ◽  
A. A. Korobkin
Keyword(s):  
Degrees Of Freedom ◽  
Early Stage ◽  
Three Dimensional ◽  
Vertical Displacement ◽  
Oblique Impact ◽  
Water Entry ◽  
The Body ◽  
Body Motion ◽  
Elliptic Paraboloid ◽  
Over Time

The water entry of a three-dimensional smooth body into initially calm water is examined. The body can move freely in its 6 d.f. and may also change its shape over time. During the early stage of penetration, the shape of the body is approximated by a surface of double curvature and the radii of curvature may vary over time. Hydrodynamic loads are calculated by the Wagner theory. It is shown that the water entry problem with arbitrary kinematics of the body motion, can be reduced to the vertical entry problem with a modified vertical displacement of the body and an elliptic region of contact between the liquid and the body surface. Low pressure occurrence is determined; this occurrence can precede the appearance of cavitation effects. Hydrodynamic forces are analysed for a rigid ellipsoid entering the water with 3 d.f. Experimental results with an oblique impact of elliptic paraboloid confirm the theoretical findings. The theoretical developments are detailed in this paper, while an application of the model is described in electronic supplementary materials.

A Biomechanical Assessment of the Sliding Motion of Curling Delivery in Elite and Subelite Curlers

2012 ◽  
Vol 28 (6) ◽  
pp. 694-700 ◽  
Author(s):  
Kyoung-Seok Yoo ◽  
Hyun-Kyung Kim ◽  
Jin-Hoon Park
Keyword(s):  
Balance Control ◽  
Center Of Mass ◽  
Three Dimensional ◽  
The Body ◽  
Movement Speed ◽  
Biomechanical Assessment ◽  
Sliding Motion ◽  
Angular Velocities ◽  
Posterior Direction ◽  
The Moment

The present study examined the technical characteristics of sliding performance from push-off until stone release in curling delivery. Five elite performance level curlers (> 7 years experience) and five subelite level curlers (< 3 years experience) were analyzed during the action of delivery of a curling stone. The joint angles, angular velocities, and moments of the body center of mass (COM) were determined based on three-dimensional kinematic data. The plantar pressure data were measured using a validated in-shoe system. The results indicated that the gliding time and horizontal velocity of the mass center of the body during the sliding phase were not significantly different between the elite and subelite groups. However, there were significant differences in the gliding distance and the rate of changes in velocity profiles of body COM between the two groups. The moment of the body COM from its relative position to the ankle of the support limb in the anterior/posterior direction was positive in elite curlers and negative in subelite curlers. In addition, larger ankle dorsiflexion and greater contact area of the sliding foot were observed in elite curlers. These data suggest a superior ability of elite curlers to maintain a regulated movement speed and balance control during the performance of a curling stone delivery.

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