scholarly journals Simultaneous Collision of the Rigid Body at Two Points

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1924
Author(s):  
Ionuț-Bogdan Dragna ◽  
Nicolae Pandrea ◽  
Nicolae-Doru Stănescu
Keyword(s):  
Kinetic Energy ◽  
Rigid Body ◽  
Coefficient Of Restitution ◽  
Numerical Results ◽  
Matrix Form ◽  
General Algorithm ◽  
New Approach ◽  
Main Assumption ◽  
Contact Points

We present a new approach based on the notion of inertance for the simultaneous collisions without friction of a rigid solid. The calculations are performed using the screw (plückerian) coordinates, while the results are obtained in matrix form, and they may be easily implemented for different practical situations. One calculates the velocities after collision, the energy of lost velocities, and the loss of the kinetic energy. The general algorithm of calculation is described in the paper. The main assumption is that the normal velocities at the contact points vanish simultaneously. The coefficients of restitution at the contact points may be equal or not. Some completely solved applications are also presented, and the numerical results are discussed. The numerical values depend on which coefficient of restitution is used.

Analysis of Force Distribution in Grasps Using Augmentation

1996 ◽  
Vol 210 (1) ◽  
pp. 15-22 ◽  
Author(s):  
J S Dai ◽  
D R Kerr
Keyword(s):  
Rigid Body ◽  
Equilibrium Condition ◽  
Jacobian Matrix ◽  
Point Contact ◽  
Force Distribution ◽  
Mathematical Basis ◽  
New Approach ◽  
Contact Points ◽  
Geometric Compatibility ◽  
Force Equilibrium

A new approach to the analysis of statically indeterminate restraint of a rigid body with any arrangement of point contact is presented in this paper. The paper associates the elasticity at restraint contacts with geometric compatibility of the contact points and constructs elastic compatibility equations, which are complementary to the restraint equations. The equations so obtained are then used to augment the restraint equations and lead to an agumented Jacobian matrix. The new approach enables grasps to be analysed and synthesized in a constraint of combined elasticity and geometric compatibility, in addition to the force equilibrium condition. This gives a mathematical basis for the analysis of force distribution of the statically indeterminate restraint. Detailed reasoning and derivations are given followed by both planar and spatial examples.

A new approach in the study of frictionless collisions using inertances

2014 ◽  
Vol 229 (12) ◽  
pp. 2144-2157 ◽  
Author(s):  
Nicolae Pandrea ◽  
Nicolae-Doru Stănescu
Keyword(s):  
Kinetic Energy ◽  
Practical Problem ◽  
Rigid Bodies ◽  
Matrix Form ◽  
New Approach ◽  
Numerical Examples ◽  
Bilateral Constraints ◽  
Complete Study

This paper presents a complete study on the collision without friction of two rigid bodies with and without bilateral constraints. Our goal is to obtain the same formulae for the impulse, the energy of the lost velocities, and the loss of kinetic energy as in the case of the collision of two particles. The study is performed with the aid of the notion of inertance. The dependence on the constraints is given by the inertances. The calculations are realized using the results from the theory of screws (plückerian coordinates). The obtained formulae are general, written in matrix form, and they may be easily used in any practical problem. We give the general algorithms for the collision of two rigid bodies with and without bilateral constraints. The equality of the coefficients of restitution in the Newton, Poisson, and energetic models is also proved. The numerical examples highlight the theory.

A new approach in the study of the collisions with friction using inertances

2018 ◽  
Vol 233 (3) ◽  
pp. 817-834 ◽  
Author(s):  
Nicolae Pandrea ◽  
Nicolae-Doru Stănescu
Keyword(s):  
Kinetic Energy ◽  
Coefficient Of Friction ◽  
Coefficient Of Restitution ◽  
Rigid Bodies ◽  
Dynamic Parameters ◽  
New Approach ◽  
Numerical Example ◽  
Complete Study ◽  
Collision With Friction

This paper presents a complete study on the collision with friction of one or two rigid bodies without constraints. The differential formula between the velocities and impulse uses the notion of inertance resulting from the theory of screws (Plückerian coordinates). One thus may calculate the kinematic and dynamic parameters, the velocities and the kinetic energies of the two rigid solids after the collision, and the variation of the kinetic energy. The calculation is detailed for the Newton, Poisson, and energetic variants of the coefficient of restitution. The variation of the kinematic and dynamic parameters in relation to the coefficient of restitution and coefficient of friction for all the three variants are presented and discussed. A numerical example highlights the theory.

An implicit scheme for simulation of free surface non-Newtonian fluid flows on dynamically adapted grids

2021 ◽  
Vol 36 (3) ◽  
pp. 165-176
Author(s):  
Kirill Nikitin ◽  
Yuri Vassilevski ◽  
Ruslan Yanbarisov
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Newtonian Fluid ◽  
Viscoelastic Fluid ◽  
Fluid Flows ◽  
Numerical Results ◽  
Implicit Scheme ◽  
New Approach

Abstract This work presents a new approach to modelling of free surface non-Newtonian (viscoplastic or viscoelastic) fluid flows on dynamically adapted octree grids. The numerical model is based on the implicit formulation and the staggered location of governing variables. We verify our model by comparing simulations with experimental and numerical results known from the literature.

scholarly journals Slipping–rolling transitions of a body with two contact points

2021 ◽  
Author(s):  
Mate Antali ◽  
Gabor Stepan
Keyword(s):  
Rigid Body ◽  
Contact Point ◽  
Static Friction ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Friction Forces ◽  
Contact Points ◽  
Body Dynamics ◽  
Coulomb Model ◽  
Rigid Surfaces

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

On Sculling Propulsion by Two Elastically Coupled Profiles

1983 ◽  
Vol 27 (02) ◽  
pp. 135-146
Author(s):  
J. A. Sparenberg ◽  
J. de Vries
Keyword(s):  
Kinetic Energy ◽  
Numerical Results ◽  
Left Behind

The sculling propulsion of two profiles which are coupled by an elastic hinge is considered. The leading profile carries out a prescribed motion. The motion of the second profile is induced by the hinge and by the fluid pressures. This profile regains part of the kinetic energy left behind by the first one. Numerical results are given.

scholarly journals The Rotating Rigid Body Model Based on a Non-twisting Frame

2020 ◽  
Vol 30 (6) ◽  
pp. 3199-3233 ◽  
Author(s):  
Cristian Guillermo Gebhardt ◽  
Ignacio Romero
Keyword(s):  
Kinetic Energy ◽  
Rigid Body ◽  
Conservation Laws ◽  
Rotation Rate ◽  
Governing Equations ◽  
New Model ◽  
Body Model ◽  
Integration Schemes ◽  
Rigid Body Model ◽  
Unit Vectors

Abstract This work proposes and investigates a new model of the rotating rigid body based on the non-twisting frame. Such a frame consists of three mutually orthogonal unit vectors whose rotation rate around one of the three axis remains zero at all times and, thus, is represented by a nonholonomic restriction. Then, the corresponding Lagrange–D’Alembert equations are formulated by employing two descriptions, the first one relying on rotations and a splitting approach, and the second one relying on constrained directors. For vanishing external moments, we prove that the new model possesses conservation laws, i.e., the kinetic energy and two nonholonomic momenta that substantially differ from the holonomic momenta preserved by the standard rigid body model. Additionally, we propose a new specialization of a class of energy–momentum integration schemes that exactly preserves the kinetic energy and the nonholonomic momenta replicating the continuous counterpart. Finally, we present numerical results that show the excellent conservation properties as well as the accuracy for the time-discretized governing equations.

Designing Planar Mechanisms Using a Bi-Invariant Metric in the Image Space of SO (3)

1994 ◽  
Author(s):  
Pierre Larochelle ◽  
J. Michael McCarthy
Keyword(s):  
Rigid Body ◽  
Numerical Results ◽  
Image Space ◽  
Dimensional Synthesis ◽  
Invariant Metric ◽  
Planar Mechanisms ◽  
Position And Orientation ◽  
Position Synthesis

Abstract In this paper we present a technique for using a bi-invariant metric in the image space of spherical displacements for designing planar mechanisms for n (> 5) position rigid body guidance. The goal is to perform the dimensional synthesis of the mechanism such that the distance between the position and orientation of the guided body to each of the n goal positions is minimized. Rather than measure these distances in the plane, we introduce an approximating sphere and identify rotations which are equivalent to the planar displacements to a specified tolerance. We then measure distances between the rigid body and the goal positions using a bi-invariant metric on the image space of SO(3). The optimal linkage is obtained by minimizing this distance over all of the n goal positions. The paper proceeds as follows. First, we approximate planar rigid body displacements with spherical displacements and show that the error induced by such an approximation is of order 1/R2, where R is the radius of the approximating sphere. Second, we use a bi-invariant metric in the image space of spherical displacements to synthesize an optimal spherical 4R mechanism. Finally, we identify the planar 4R mechanism associated with the optimal spherical solution. The result is a planar 4R mechanism that has been optimized for n position rigid body guidance using an approximate bi-invariant metric with an error dependent only upon the radius of the approximating sphere. Numerical results for ten position synthesis of a planar 4R mechanism are presented.

Thermodynamics From a Few Dynamic Particles Raises Questions as to How Temperature and Entropy Should Be Perceived and Defined

2007 ◽  
Author(s):  
W. John Dartnall ◽  
John Reizes
Keyword(s):  
Kinetic Energy ◽  
Single Particle ◽  
Heat Engine ◽  
Working Fluid ◽  
Second Law ◽  
Piston Engine ◽  
New Approach ◽  
Particle Mechanics ◽  
Mechanics Model ◽  
Heat Engines

In a recently developed simple particle mechanics model, in which a single particle represents the working fluid, (gas) in a heat engine, (exemplified by a piston engine) a new approach was outlined for the teaching of concepts to thermodynamic students. By mechanics reasoning, a model was developed that demonstrates the connection between the Carnot efficiency limitation of heat engines, and the Kelvin-Planck statement of Second Law, requiring only the truth of the Clausius statement. In a second paper the model was extended to introduce entropy. The particle’s entropy was defined as a function of its kinetic energy, and the space that it occupies, that is analogous to that normally found in classical macroscopic analyses. In this paper, questions are raised and addressed: How should temperature and entropy be perceived and defined? Should temperature be proportional to average (molecular) translational kinetic energy and should entropy be dimensionless?

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