Reduction of Arbitrary Rigid Bodies to Inertially Equivalent Discrete Systems of Material Points

2015 ◽  
Vol 762 ◽  
pp. 33-40
Author(s):  
Andrei Craifaleanu ◽  
Nicolaie Orăşanu
Keyword(s):  
Center Of Mass ◽  
Discrete Systems ◽  
Rigid Bodies ◽  
The Body ◽  
Plane Plate ◽  
Rigid Plane ◽  
Arbitrary Body ◽  
Material Points ◽  
Cartesian Coordinate ◽  
Mechanical Devices

In a previous paper of the authors, a general method was presented for the reduction of a rigid plane plate to a discrete system of material points, with equivalent inertial properties (mass, center of mass, tensor of inertia). The present paper generalizes the method for rigid bodies of arbitrary shape, i.e. for material volumes, as well as for curved shells. It is shown that a homogenous ellipsoid can be reduced to a system of seven material points placed in significant geometrical points of the body. Next, starting from the concept of ellipsoid of inertia, an equivalent homogenous ellipsoid is determined for an arbitrary body. The method simplifies considerably the calculation of various mechanical quantities, such as moments and products of inertia with respect to rotated Cartesian coordinate systems, angular momentum and kinetic energy, of rigid bodies part of all types of mechanical devices or structures.

Use of Equimomental Systems in Calculating Inertial and Dynamic Quantities of Plane Plates

2014 ◽  
Vol 555 ◽  
pp. 458-465 ◽  
Author(s):  
Nicolaie Orăşanu ◽  
Andrei Craifaleanu
Keyword(s):  
Arbitrary Shape ◽  
Center Of Mass ◽  
Industrial Robots ◽  
Elliptical Plate ◽  
Reduction Procedure ◽  
Plane Plate ◽  
Rigid Plane ◽  
Material Points ◽  
Complex Mechanical Systems ◽  
Tensor Of Inertia

The paper proposes a method for the reduction of an arbitrary-shape plane plate to a symmetrical discrete system of material points, with the same center of mass and the same tensor of inertia. It is shown, first, that an elliptical plate can be reduced to a symmetrical system of five material points, with a spatial distribution directly related to the shape of the plate. The results are subsequently generalized for plane plates of arbitrary shape. By using the reduction procedure, various mechanical quantities can be calculated more simply, as compared to the traditional methods. The proposed method finds application in the dynamic, vibration and structural analysis of complex mechanical systems that include rigid plane plates, such as industrial robots.

Die Pauli-Gleichung mit Differentialoperatoren für den Spin/ The Pauli Equation with Differential Operators for the Spin

1978 ◽  
Vol 33 (10) ◽  
pp. 1133-1150
Author(s):  
Eberhard Kern
Keyword(s):  
Angular Momentum ◽  
Rigid Body ◽  
Differential Operators ◽  
Spin Operator ◽  
Rigid Bodies ◽  
The Body ◽  
Wave Functions ◽  
Pauli Equation ◽  
Spin Eigenfunctions ◽  
Cartesian Coordinate

The spin operator s = (ħ/2) σ in the Pauli equation fulfills the commutation relation of the angular momentum and leads to half-integer eigenvalues of the eigenfunctions for s. If one tries to express s by canonically conjugated operators Φ and π = (ħ/i) ∂/∂Φ the formal angular momentum term s = Φ X π fails because it leads only to whole-integer eigenvalues. However, the modification of this term in the form s = 1/2 {π + Φ(Φ π) + Φ X π} leads to the required result.The eigenfunction system belonging to this differential operator s(Φ π) consists of (2s + 1) spin eigenfunctions ξm (Φ) which are given explicitly. They form a basis for the wave functions of a particle of spin s. Applying this formalism to particles with s = 1/2, agreement is reached with Pauli’s spin theory.The function s(Φ π) follows from the theory of rotating rigid bodies. The continuous spinvariable Φ = ((Φx , Φy, Φz) can be interpreted classically as a “turning vector” which defines the orientation in space of a rigid body. Φ is the positioning coordinate of the rigid body or the spin coordinate of the particle in analogy to the cartesian coordinate x. The spin s is a vector fixed to the body.

Uncertainty Reduction on the Identification of the Inertial Parameters Based on a Complex 3D Motion

2010 ◽  
Author(s):  
Juan P. Barreto M. ◽  
Luis E. Munoz C.
Keyword(s):  
Center Of Mass ◽  
Algebraic Method ◽  
Rigid Bodies ◽  
The Body ◽  
Inertia Tensor ◽  
Identification System ◽  
3D Motion ◽  
Inertial Parameters ◽  
Static Experiment ◽  
Measuring Unit

The uncertainty on the identification of the inertial parameters of rigid bodies can be reduced by studying the motion for the identification experiments. This paper presents a method for measuring the center of mass and the inertia tensor of a rigid body by generating a complex 3D motion. The proposed method is intended to reduce the time consumed by the experiment and the post-processing of the data. This reduction on the time is achieved by using the same assembly for the center of mass and inertia tensor identification experiments as well as an algebraic method for the identification. The experimental setup consists on a Stewart Platform for the generation of the motion, a load cell and an inertial measuring unit. A study on the reduction of the uncertainty was developed. It was found that the uncertainty on the identification of the center of mass can be reduced with a static experiment that takes the object to different orientations, improving the numerical condition of the identification system. The uncertainty on the inertia tensor identification is reduced when the motion of the body is generated relative to different axes in space. The method was first tested on simulations to estimate the uncertainty and then validated experimentally.

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

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 Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 531
Author(s):  
Pedro Pablo Ortega Palencia ◽  
Ruben Dario Ortiz Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Negative Curvature ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Simple Expression ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Euclidean Case ◽  
System Of Particles ◽  
Material Points ◽  
The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

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 An Unstructured Finite Volume Method for Incompressible Flows With Complex Immersed Boundaries

2009 ◽  
Author(s):  
Lin Sun ◽  
Sanjay R. Mathur ◽  
Jayathi Y. Murthy
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Incompressible Flows ◽  
Simple Algorithm ◽  
Flow Region ◽  
Solid Material ◽  
The Body ◽  
Immersed Boundary ◽  
Material Points ◽  
Volume Method

A numerical method is developed for solving the 3D, unsteady, incompressible flows with immersed moving solids of arbitrary geometrical complexity. A co-located (non-staggered) finite volume method is employed to solve the Navier-Stokes governing equations for flow region using arbitrary convex polyhedral meshes. The solid region is represented by a set of material points with known position and velocity. Faces in the flow region located in the immediate vicinity of the solid body are marked as immersed boundary (IB) faces. At every instant in time, the influence of the body on the flow is accounted for by reconstructing implicitly the velocity the IB faces from a stencil of fluid cells and solid material points. Specific numerical issues related to the non-staggered formulation are addressed, including the specification of face mass fluxes, and corrections to the continuity equation to ensure overall mass balance. Incorporation of this immersed boundary technique within the framework of the SIMPLE algorithm is described. Canonical test cases of laminar flow around stationary and moving spheres and cylinders are used to verify the implementation. Mesh convergence tests are carried out. The simulation results are shown to agree well with experiments for the case of micro-cantilevers vibrating in a viscous fluid.

scholarly journals Modeling of strains and stresses of material nanostructures

2009 ◽  
Vol 57 (1) ◽  
pp. 41-46
Author(s):  
G. Szefer ◽  
D. Jasińska
Keyword(s):  
Materials Science ◽  
Discrete Systems ◽  
Deformation Analysis ◽  
Model Description ◽  
Atomic Interactions ◽  
Stress And Deformation ◽  
Material Points ◽  
Graphite Sheets ◽  
Intense Research ◽  
Nanoscale Level

Modeling of strains and stresses of material nanostructuresStress and deformation analysis of materials and devices at the nanoscale level are topics of intense research in materials science and mechanics. In these investigations two approaches are observed. First, natural for the atomistic scale description is based on quantum and molecular mechanics. Second, characteristic for the macroscale continuum model description, is modified by constitutive laws taking atomic interactions into account. In the present paper both approaches are presented. For a discrete system of material points (atoms, molecules, clusters), measures of strain and stress, important from the mechanical viewpoint, are given. Numerical examples of crack propagation and deformation of graphite sheets (graphens) illustrate the behavior of the discrete systems.

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.

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