Nonaxisymmetric Acoustic Radiation and Scattering From Rigid Bodies of Revolution Using the Surface Variational Principle

1998 ◽  
Vol 120 (1) ◽  
pp. 95-103 ◽  
Author(s):  
J. H. Ginsberg ◽  
Kuangcheng Wu
Keyword(s):  
Variational Principle ◽  
Rigid Body ◽  
Acoustic Radiation ◽  
Axisymmetric Body ◽  
Rigid Bodies ◽  
Body Motion ◽  
Convergence Properties ◽  
Bodies Of Revolution ◽  
Computer Codes ◽  
Acoustic Fluid

The surface variational principle (SVP), which represents the surface response as a series of basis functions spanning the entire surface, provides a global description of acoustic fluid-structure interaction that has many of the benefits associated with analytical methods. This paper describes the extension of SVP to model the interaction between the velocity and pressure on the surface of an axisymmetric body subjected to nonaxisymmetric excitation. Problems addressed are radiation due to arbitrary rigid body motion, and scattering associated with arbitrary incidence of a plane wave on a stationary rigid body. Numerical results are presented for flat-ended and hemi-capped cylinders. These results are compared to those obtained from the CHIEF-88 and SHIP-92 computer codes. The convergence properties of SVP are examined in detail, particularly for its requirements when ka is in the upper part of the mid-frequency range.

On Higher Order Point-Line and the Associated Rigid Body Motions

2006 ◽  
Vol 129 (2) ◽  
pp. 166-172 ◽  
Author(s):  
Yi Zhang ◽  
Kwun-Lon Ting
Keyword(s):  
Rigid Body ◽  
Higher Order ◽  
Rigid Bodies ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Dual Quaternion ◽  
Displacement Operator ◽  
Screw Motion ◽  
Rigid Body Motions ◽  
Point Line

This paper presents a study on the higher-order motion of point-lines embedded on rigid bodies. The mathematic treatment of the paper is based on dual quaternion algebra and differential geometry of line trajectories, which facilitate a concise and unified description of the material in this paper. Due to the unified treatment, the results are directly applicable to line motion as well. The transformation of a point-line between positions is expressed as a unit dual quaternion referred to as the point-line displacement operator depicting a pure translation along the point-line followed by a screw displacement about their common normal. The derivatives of the point-line displacement operator characterize the point-line motion to various orders with a set of characteristic numbers. A set of associated rigid body motions is obtained by applying an instantaneous rotation about the point-line. It shows that the ISA trihedrons of the associated rigid motions can be simply depicted with a set of ∞2 cylindroids. It also presents for a rigid body motion, the locus of lines and point-lines with common rotation or translation characteristics about the line axes. Lines embedded in a rigid body with uniform screw motion are presented. For a general rigid body motion, one may find lines generating up to the third order uniform screw motion about these lines.

A Computationally Efficient Planar Rigid Body Velocity Measure

2009 ◽  
Author(s):  
Luis E. Criales ◽  
Joseph M. Schimmels
Keyword(s):  
Rigid Body ◽  
Rigid Bodies ◽  
Body Motion ◽  
Computationally Efficient ◽  
Straight Line ◽  
Body Velocity ◽  
Velocity Measure ◽  
Rigid Body Motions ◽  
Line Path ◽  
Planar Motions

A planar rigid body velocity measure based on the instantaneous velocity of all particles that constitute a rigid body is developed. This measure compares the motion of each particle to an “ideal”, but usually unobtainable, motion. This ideal motion is one that would carry each particle from its current position to its desired position on a straight-line path. Although the ideal motion is not a valid rigid body motion, this does not preclude its use as a reference standard in evaluating valid rigid body motions. The optimal instantaneous planar motions for general rigid bodies in translation and rotation are characterized. Results for an example planar positioning problem are presented.

Paradoxes in Rigid-Body Kinematics of Structures

1998 ◽  
Vol 65 (1) ◽  
pp. 218-222
Author(s):  
L. Mentrasti
Keyword(s):  
Rigid Body ◽  
Kinematic Analysis ◽  
Sufficient Conditions ◽  
Rigid Bodies ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Kinematic Chains ◽  
Straight Line ◽  
Two Bodies

The paper discusses two paradoxes appearing in the kinematic analysis of interconnected rigid bodies: there are structures that formally satisfy the classical First and Second Theorem on kinematic chains, but do not have any motion. This can arise when some centers of instantaneous rotation (CIR) relevant to two bodies coincide with each other (first kind paradox) or when the CIRs relevant to three bodies lie on a straight line (second kind paradox). In these cases two sets of new theorems on the CIRs can be applied, pointing out sufficient conditions for the nonexistence of a rigid-body motion. The question is clarified by applying the presented theory to several examples.

The Design of an Augmented Reality Based Rigid Body Motion Experiment System

2015 ◽  
Vol 719-720 ◽  
pp. 275-278
Author(s):  
Yang Xiang Zhang ◽  
Yun Zhu ◽  
Hui Ye
Keyword(s):  
Augmented Reality ◽  
Rigid Body ◽  
Real Time ◽  
Rigid Bodies ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Motion Information ◽  
Experiment System ◽  
The Real ◽  
Physical Motion

The authors have designed an augmented reality based rigid body motion experiment system (ARRBMES), which could capture the physical motion information from the interaction between the users and virtual rigid bodies in real-time. The launcher and the container of the rigid bodies in this system are all positioned by tag cards, and the initial physical quantities of the rigid bodies are captured and analyzed through the motion information of the launcher tag card. Then ARRBMES will realize the real-time display of rigid body motion and collision events in a virtual-real fusion environment. ARRBMES can simulate the motion of rigid bodies in ideal state which cannot be achieved in the real world. As a result, the users can obtain realistic experience and the system can increase their physical intuition and cognitive experience. Moreover, ARRBMES can obtain physical information from the interaction in real-time between users and the system, which makes it a special Cyber-Physical System.

scholarly journals On the Hamel Coefficients and the Boltzmann–Hamel Equations for the Rigid Body

2021 ◽  
Vol 31 (2) ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Rigid Body ◽  
Nonholonomic Systems ◽  
Rigid Bodies ◽  
Body Motion ◽  
Floating Body ◽  
Lagrange Equations ◽  
Local Coordinates ◽  
Dynamics And Control ◽  
Boltzmann Hamel Equations ◽  
And Control

AbstractThe Boltzmann–Hamel (BH) equations are central in the dynamics and control of nonholonomic systems described in terms of quasi-velocities. The rigid body is a classical example of such systems, and it is well-known that the BH-equations are the Newton–Euler (NE) equations when described in terms of rigid body twists as quasi-velocities. It is further known that the NE-equations are the Euler–Poincaré, respectively, the reduced Euler–Lagrange equations on SE(3) when using body-fixed or spatial representation of rigid body twists. The connection between these equations are the Hamel coefficients, which are immediately identified as the structure constants of SE(3). However, an explicit coordinate-free derivation has not been presented in the literature. In this paper the Hamel coefficients for the rigid body are derived in a coordinate-free way without resorting to local coordinates describing the rigid body motion. The three most relevant choices of quasi-velocities (body-fixed, spatial, and hybrid representation of rigid body twists) are considered. The corresponding BH-equations are derived explicitly for the rotating and free floating body. Further, the Hamel equations for nonholonomically constrained rigid bodies are discussed, and demonstrated for the inhomogenous ball rolling on a plane.

Numerical and Experimental Approaches on the Motion of a Tethered System With Large Deformation, Rotation and Translation

2005 ◽  
Author(s):  
Shoichiro Takehara ◽  
Yoshiaki Terumichi ◽  
Masahiro Nohmi ◽  
Kiyoshi Sogabe ◽  
Yoshihiro Suda
Keyword(s):  
Rigid Body ◽  
Large Deformation ◽  
Numerical Solutions ◽  
Rigid Bodies ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Flexible Body ◽  
Numerical Formulation ◽  
Experimental Approaches ◽  
Good Agreement

In this paper, we discuss the motion of a tethered system. In general, a tether is a cable or wire rope, and a tethered system consists of a tether and attached equipment. A tethered subsatellite in space is an example of this system. We consider the tethered system consisting of a very flexible body (the tether) and rigid bodies at one end as our analytical model. A flexible body in planer motion is described using the Absolute Nodal Coordinate Formulation. Using this method, the motion of a flexible body with large deformation, rotation and translation can be expressed with the accuracy of rigid body motion. The combination of flexible body motion and rigid body motion is performed and the interaction between them is discussed. We also performed experiments to investigate the fundamental motion of the tethered system and to evaluate the validity of the numerical formulation. The first experiments were conducted using a steel tether and rubber tether in gravity space. We also conducted experiment of the motion of the tethered system with a rigid body in microgravity space. The numerical solutions using the proposed methods for the modeling and formulation for the tethered system are in good agreement with the experimental results.

Lumped-Parameter Modelling of Spatial Compliance Using a Twist-Based Potential Function

1999 ◽  
Author(s):  
Ernest D. Fasse ◽  
Shilong Zhang
Keyword(s):  
Rigid Body ◽  
Potential Function ◽  
Quadratic Function ◽  
Rigid Bodies ◽  
Body Motion ◽  
Active Compliance ◽  
Lumped Parameter ◽  
Rigid Body Displacement ◽  
Robotic Devices ◽  
Spatial Compliance

Abstract This paper examines geometric modelling of elastically coupled, spatial rigid body pairs. For a pair of elastically coupled rigid bodies there exist coincident, unique points on the bodies or their rigid extensions known as centers of stiffness at which translation and rotation are minimally coupled. The rigid body displacement of frames at the centers of stiffness can be associated with a twist displacement, a continuous rigid body motion. A potential function is defined that is a simple quadratic function of the twist displacement. Constitutive equations relating rigid body displacement and wrench are derived. While the problem of modelling and computer simulation is emphasized, the work is also relevant for active compliance control of robotic devices.

scholarly journals Modeling and Prediction of Rigid Body Motion with Planar Non-Convex Contact

2021 ◽  
pp. 1-17
Author(s):  
Jiayin Xie ◽  
Nilanjan Chakraborty
Keyword(s):  
Rigid Body ◽  
Dynamic Simulation ◽  
Contact Region ◽  
Contact Point ◽  
Single Point ◽  
Point Contact ◽  
Rigid Bodies ◽  
Body Motion ◽  
Contact Patch ◽  
Connected Set

Abstract We present a principled method for motion prediction via dynamic simulation for rigid bodies in intermittent contact with each other where the contact region is a planar non-convex contact patch. Such methods are useful in planning and control for robotic manipulation. The planar non-convex contact patch can either be a topologically connected set or disconnected set. Most work in rigid body dynamic simulation assume that the contact between objects is a point contact, which may not be valid in many applications. In this paper, by using the convex hull of the contact patch, we build on our recent work on simulating rigid bodies with convex contact patches for simulating motion of objects with planar non-convex contact patches. We formulate a discrete-time mixed complementarity problem where we solve the contact detection and integration of the equations of motion simultaneously. We solve for the equivalent contact point (ECP) and contact impulse of each contact patch simultaneously along with the state, i.e., configuration and velocity of the objects. We prove that although we are representing a patch contact by an equivalent point, our model for enforcing non-penetration constraints ensure that there is no artificial penetration between the contacting rigid bodies. We provide empirical evidence to show that our method can seamlessly capture transition among different contact modes like patch contact, multiple or single point contact.

The electrophoretic mobility of rod-like particles

2013 ◽  
Vol 719 ◽  
Author(s):  
Ehud Yariv ◽  
Ory Schnitzer
Keyword(s):  
Rigid Body ◽  
Arbitrary Shape ◽  
Symmetry Axis ◽  
Body Motion ◽  
Spherical Particles ◽  
Rectilinear Motion ◽  
Body Rotation ◽  
Cross Sectional ◽  
Bodies Of Revolution ◽  
Specific Particle

AbstractAt finite Dukhin numbers, where Smoluchowski’s formula is inapplicable to thin-double-layer electrophoresis, the mobility of non-spherical particles is generally anisotropic. We consider bodies of revolution of otherwise arbitrary shape, where a uniformly applied electric field results in a rectilinear motion in the plane spanned by the field direction and the particle symmetry axis, as well as (for particles lacking fore–aft symmetry) rigid-body rotation about an axis perpendicular to that plane. Focusing upon slender particles, where the ratio $\epsilon $ of cross-sectional and longitudinal scales is asymptotically small, the translational and rotational mobilities are obtained as quadratures which depend upon the lengthwise distribution of the scaled cross-sectional width and the force densities associated with rigid-body motion. These mobility expressions approach finite limits as $\epsilon \rightarrow 0$, yielding closed-form expressions for specific particle geometries.

scholarly journals SOME PROBLEMS ABOUT THE MOTION OF A RIGID BODY IN A RESISTIVE MEDIUM

2021 ◽  
Vol 3 (2) ◽  
pp. 6-17
Author(s):  
D. Leshchenko ◽  
◽  
T. Kozachenko ◽  
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Modern Technology ◽  
Rigid Bodies ◽  
Rigid Body Motion ◽  
The Body ◽  
Body Motion ◽  
Body Rotation ◽  
Angular Velocity Vector ◽  
Resistive Medium

The dynamics of rotating rigid bodies is a classical topic of study in mechanics. In the eighteenth and nineteenth centuries, several aspects of a rotating rigid body motion were studied by famous mathematicians as Euler, Jacobi, Poinsot, Lagrange, and Kovalevskya. However, the study of the dynamics of rotating bodies of still important for aplications such as the dynamics of satellite-gyrostat, spacecraft, re-entry vehicles, theory of gyroscopes, modern technology, navigation, space engineering and many other areas. A number of studies are devoted to the dynamics of a rigid body in a resistive medium. The presence of the velocity of proper rotation of the rigid body leads to the apearance of dissipative torques causing the braking of the body rotation. These torques depend on the properties of resistant medium in which the rigid body motions occur, on the body shape, on the properties of the surface of the rigid body and the distribution of mass in the body and on the characters of the rigid body motion. Therefore, the dependence of the resistant torque on the orientation of the rigid body and its angular velocity can de quite complicated and requires consideration of the motion of the medium around the body in the general case. We confine ourselves in this paper to some simple relations that can qualitative describe the resistance to rigid body rotation at small angular velocities and are used in the literature. In setting up the equations of motion of a rigid body moving in viscous medium, we need to consider the nature of the resisting force generated by the motion of the rigid body. The evolution of rotations of a rigid body influenced by dissipative disturbing torques were studied in many papers and books. The problems of motion of a rigid body about fixed point in a resistive medium described by nonlinear dynamic Euler equations. An analytical solution of the problem when the torques of external resistance forces are proportional to the corresponding projections of the angular velocity of the rigid body is obtain in several works. The dependence of the dissipative torque of the resistant forces on the angular velocity vector of rotation of the rigid body is assumed to be linear. We consider dynamics of a rigid body with arbitrary moments of inertia subjected to external torques include small dissipative torques.

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