scholarly journals Note on an Equation of Motion

1890 ◽  
Vol 9 ◽  
pp. 91-92
Author(s):  
A. J. Pressland
Keyword(s):  
Relative Motion ◽  
Equation Of Motion ◽  
Third Body ◽  
Straight Line ◽  
Two Bodies

It can be shown by means of relative motion that if two bodies A and B move with velocities u and v in the same straight line, and a third body C move with velocity u + v also in the same straight line, the space passed over by C is equal to the sum of the spaces passed over by A and by B in the same time.

Application of Dry-Friction Whip and Whirl Solution Methods to Systems With Support Asymmetry

2018 ◽  
Author(s):  
Jason C. Wilkes
Keyword(s):  
Relative Motion ◽  
General Model ◽  
Dry Friction ◽  
Current Work ◽  
General Sense ◽  
Continuous Contact ◽  
Solution Methods ◽  
Asymmetric Rotor ◽  
Two Bodies

Dry-friction whip and whirl occurs when a rotor contacts a stator across a clearance annulus. In a general sense, the relative motion between the two bodies is described by a circular precessing motion. While this problem is generally well understood, the author is unaware of any papers that discuss the problem for systems having asymmetric rotor or stator supports. The current work will investigate a general model to describe dry-friction whip and whirl for the case of continuous contact between a rotor and stator in the presence of asymmetry. This paper will show that for light asymmetry, the rotor and stator motions are elliptical; however, the relative motion between the two bodies remains circular.

Formulas for Entraining Velocity in Lubricated Line Contacts

2002 ◽  
Vol 124 (4) ◽  
pp. 856-858
Author(s):  
Enrico Ciulli
Keyword(s):  
Relative Motion ◽  
Physical Meaning ◽  
Point Of View ◽  
Lubricated Contacts ◽  
Line Contacts ◽  
Two Bodies

The knowledge of the entraining velocity is necessary for the investigation of lubricated contacts. The entraining velocity is the average of the surface velocities of the two bodies in contact relative to the contact itself; its estimation can be actually not always immediate. In this work the general case of two pairing cylindrical surfaces in planar relative motion is analyzed from a kinematical point of view. Formulas for the evaluation of the entraining velocity are presented that are directly applicable to any case of connected members of a mechanism. The physical meaning of the terms of the proposed formulas is also briefly investigated from a lubrication point of view.

Extended Camus Theory and Higher Order Conjugated Curves

2019 ◽  
Author(s):  
Cody Leeheng Chan ◽  
Kwun-Lon Ting
Keyword(s):  
Stationary Point ◽  
Higher Order ◽  
The Body ◽  
The Other ◽  
Body System ◽  
Straight Line ◽  
Pair Generation ◽  
Curvature Theory ◽  
Three Body ◽  
Two Bodies

Abstract According to Camus’ theorem, for a single DOF 3-body system with the three instant centers staying coincident, a point embedded on a body traces a pair of conjugated curves on the other two bodies. This paper discusses a fundamental issue not addressed in Camus’ theorem in the context of higher order curvature theory. Following the Aronhold-Kennedy theorem, in a single degree-of-freedom three-body system, the three instant centers must lie on a straight line. This paper proposes that if the line of the three instant centers is stationary (i.e. slide along itself), on the line of the instant centers a point embedded on a body traces a pair of conjugated curves on the other two bodies. Another case is that if the line of the three instant centers rotate about a stationary point, the stationary point embedded on the body also traces a pair of conjugated curves on the other two bodies. The paper demonstrates the use of instantaneous invariants to synthesize such a three-body system leading to a conjugate curve-pair generation. It is a supplement or extension of the Camus’ theorem. The Camus’ theorem may be regarded as a special singular case, in which all three instant centers are coincident.

Physico-Chemical Modeling of Third Body Rheology

2010 ◽  
Author(s):  
Mathieu Renouf
Keyword(s):  
Third Body ◽  
Unknown Parameters ◽  
Chemical Modeling ◽  
The Third ◽  
Real Contact ◽  
Physico Chemical ◽  
Role Concerns ◽  
Set Up ◽  
Discrete Element Methods ◽  
Two Bodies

The well-known concept of third body was introduced by Godet in the seventies to characterise the discontinuous and heterogeneous interface that separates two bodies in contact. This thin layer (from some nanometers to some micrometers high) appears to possess its own rheology depending of contact conditions, material properties and often, extra unknown parameters. If its main common role concerns essentially mechanical aspects such as velocity accommodation, load carrying capacity and solid lubricant, it plays an important role in other physical aspects. For example, it ensures the thermal continuity between two bodies in contact and explains the jump of temperature observed experimentally. Moreover, it is able to capture the maximal temperature through its thickness. Due to the difficulty to instrument a real contact without disturbing the local rheology, observations of the third body rheology occur only on simplified experimental set-up. To reproduce and try to understand “real contact in presence of third body”, numerical tools have been developed and adapt to face new challenge raised by the third-body concept. The discontinuity and heterogeneity of such interface led researchers to use discrete element methods (DEM) to describe its evolution. Several improvments of the method allow to deal with the mechanical and the thermal behaviour of such media but without interactions. The integration of physicochemical aspects is presented in the paper to link thermal and mechanical behaviour and proposed a model able to represent the multi-physical feature of a contact interface.

scholarly journals The noninertial origin of the reduced mass

2006 ◽  
Vol 28 (1) ◽  
pp. 123-124
Author(s):  
Valmar Carneiro Barbosa
Keyword(s):  
Relative Motion ◽  
Physical Interpretation ◽  
Particle System ◽  
Equation Of Motion

A different way to obtain the equation of motion that governs the relative motion in a two-particle system is presented. It provides the physical interpretation of the reduced mass as a noninertial effect.

Wave-Energy Conversion Through Relative Motion Between Two Single-Mode Oscillating Bodies

1999 ◽  
Vol 121 (1) ◽  
pp. 32-38 ◽  
Author(s):  
J. Falnes
Keyword(s):  
Energy Conversion ◽  
Relative Motion ◽  
Wave Energy ◽  
Load Force ◽  
Wave Forces ◽  
Equivalent System ◽  
Wave Excitation ◽  
Excitation Force ◽  
Two Bodies ◽  
Wave Excitation Force

Wave-energy converters (WECs) need a reaction source against which the wave forces can react. As with shore-based WECs, sometimes also floating WECs react against a fixed point on the seabed. Alternatively, for a floating WEC, force reaction may be obtained by utilizing the relative motion between two bodies. A load force for energy conversion is assumed to be applied only to this relative motion. It is assumed that either body oscillates in one mode only (mostly, the heave mode is considered here). The system, if assumed to be linear, is proved to be phenomenologically equivalent to a one-mode, one-body system, for which the wave excitation force equals the force which is necessary to apply between the two bodies in order to ensure that they are oscillating with zero relative motion. It is discussed how this equivalent excitation force and also the intrinsic mechanical impedance of the equivalent system depend on the mechanical impedances for the two separate bodies, including the radiation impedance matrix (which combines radiation resistances and added masses). The equivalent system is applied for discussing optimum performance for maximizing the absorbed wave energy. It is shown that, for an axisymmetric system utilizing heave modes, it is possible to absorb an energy amounting to the incident wave power on a crest length which equals the wavelength divided by 2π, even though the power take-off is applied to the relative motion only. Moreover, it is shown that it is possible to obtain an equivalent excitation force which exceeds the wave excitation force on either body.

scholarly journals A Control System For Constrained Wave-Powered Oceanographic Buoys

2020 ◽  
Vol 2 (1 (Nov)) ◽  
pp. 51-61
Author(s):  
Shangyan Zou ◽  
Ossama Abdelkhalik
Keyword(s):  
Relative Motion ◽  
Wave Energy ◽  
Control Strategy ◽  
Real Data ◽  
Nonlinear Damping ◽  
Irregular Waves ◽  
Coastal Observatory ◽  
Switching Control Strategy ◽  
Displacement Constraints ◽  
Two Bodies

Wave energy can be used to power oceanographic buoys. A new switching control strategy is developed in this paper for a two-body heaving wave energy converter that is composed of a floating cylinder and two rigidly connected submerged hemispheres. This control strategy is designed to prevent excessive displacement of the floating buoy that may occur due to the actuator force. This control strategy switches the control between a multi-resonant controller and a nonlinear damping controller, depending on the state of the system, to account for displacement constraints. This control strategy is developed using a one-degree-of-freedom dynamic model for the relative motion of the two bodies. Estimation of the relative motion, needed for feedback control, is carried out using a Kalman filter. Numerical simulations are conducted to select the proper mooring stiffness. The controller is tested with stochastic models of irregular waves in this paper. The performance of the controller with different sea states is discussed. Annual power production using this control strategy is presented based on real data in 2015 published by Martha's Vineyard Coastal Observatory.

scholarly journals New Phenomena in the Spatial Isosceles Three-Body Problem

2015 ◽  
Vol 25 (09) ◽  
pp. 1550116 ◽  
Author(s):  
Duokui Yan ◽  
Tiancheng Ouyang
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
The Other ◽  
Initial Condition ◽  
Collision Orbit ◽  
Three Body Problem ◽  
Straight Line ◽  
Three Body ◽  
New Phenomena ◽  
Two Bodies

In the three-body problem, it is known that there exists a special set of periodic orbits: spatial isosceles periodic orbits. In each period, one body moves up and down along a straight line, and the other two bodies rotate around this line. In this work, we revisit this set of orbits by applying variational method. Two unexpected phenomena are discovered. First, this set is not always spatial. It actually bifurcates from the circular Euler (central configuration) orbit to the Broucke (collision) orbit. Second, one of the orbits in this set encounters an oscillating behavior. By running its initial condition, the orbit stays periodic for only a few periods before it becomes irregular. However, it moves close to another periodic shape in a while. Shortly it falls apart again and starts running close to a third periodic shape after a moment. This oscillation continues as t increases. Actually, up to t = 1.2 × 105, the orbit is bounded and keeps oscillating between periodic shapes and irregular motions.

Velocity and Acceleration Analysis of Contact Between Three-Dimensional Rigid Bodies

1996 ◽  
Vol 63 (4) ◽  
pp. 974-984 ◽  
Author(s):  
N. Sankar ◽  
V. Kumar ◽  
Xiaoping Yun
Keyword(s):  
Rigid Body ◽  
Relative Motion ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
Local Surface ◽  
Contact Points ◽  
Pure Rolling ◽  
Acceleration Analysis ◽  
Rigid Body Motions ◽  
Two Bodies

During manipulation and locomotion tasks encountered in robotics, it is often necessary to control the relative motion between two contacting rigid bodies. In this paper we obtain the equations relating the motion of the contact points on the pair of contacting bodies to the rigid-body motions of the two bodies. The equations are developed up to the second order. The velocity and acceleration constraints for contact, for rolling, and for pure rolling are derived. These equations depend on the local surface properties of each contacting body. Several examples are presented to illustrate the nature of the equations.

scholarly journals A Contribution to Avalanche Dynamics: A Formal and an Exact Solution of the Voellmy/Perla Two-Parametric Equation of Motion (Abstract only)

1983 ◽  
Vol 4 ◽  
pp. 304
Author(s):  
Bonsak Schieldrop
Keyword(s):  
Exact Solution ◽  
Velocity Profile ◽  
Average Velocity ◽  
Equation Of Motion ◽  
Centrifugal Effect ◽  
Circular Arcs ◽  
Straight Line ◽  
Abrupt Changes ◽  
Friction Parameters ◽  
Straight Lines

The two-parameter equation of motion for snow avalanches proposed by Voellmy in 1955 was later formally derived by Perla in 1979. It has been the object of numerous investigations, mainly to its applications. It has been solved for tracks approximated by straight lines, and this solution has, in some countries, been used extensively with a two-segment approximation. Perla and Cheng programmed such a solution for digital computation by matching an arbitrary number of straight line segments. This solution can also include impact losses due to abrupt changes in the track. In the first part of this paper a formal integration of the Voellmy/Perla equation is carried out for the general case of a track. The averaged values of the different terms are discussed and evaluated as to their relative orders of magnitude. It is shown that the “centrifugal” effect, which is, of course, automatically omitted in the straight-line solution, can be neglected in most cases. As a conclusion it is shown that all avalanche motions governed by the Voellmy/Perla equation will have the same average velocity on all tracks having the same vertical drop H, the same horizontal extension L, and the same set of “friction” parameters, as long as the length S of the track is the same, regardless of the shape of the tracks. The shape will only determine the velocity profile along the track. The second part of the paper shows the exact solution of the equation for the special case of tracks with constant curvature, i.e. circular arcs. If the conclusion of the first part of the paper holds true, this solution can be used to determine the average velocity on other shaped tracks of the same length, etc. It is finally shown that a number of well-known avalanches described in the literature can well be approximated by a circular arc. In these cases even the velocity profile is determined by the exact solution.

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