Principle Of Relative Motion Research Articles

Explaining Ground Effect Aerodynamics via a Real-Life Reference Frame

The principle of relative motion as the cause of forces on a body submersedin a uid is foundational in the study of uid mechanics. In aerodynamics the wind tunnelis used as a convenient and safe method by which to test the aerodynamic performance ofbodies. This body-stationary convention has carried over into the computational world withthe development of CFD, though there is no practical reason why the moving body/stationaryuid set-up that corresponds to reality cannot be used for computational modelling. This pointbecomes particularly important as the concept of ground e ect is introduced. With an extraboundary nearby it becomes harder to appropriatel y match the experimental set-up with reality,and the extra boundary condition also adds complexity to computational simulation. A studywas undertaken to compare the body-stationary and body-moving reference frames in grounde ect. The moving reference frame velocity elds allowed new insight into the aerodynamics ofground e ect.

Numerical study of the pitching motions of supercavitating vehicles

The pitching motions of supercavitating vehicles could not be avoided due to the lost water buoyancy. In order to have some insight for the design of the supercavitating vehicles, the fixed frequency and free pitching motions are investigated. A numerical predicting method based on the relative motion principle and the non-inertia coordinate system is proposed to simulate the free pitching motions of supercavitating vehicles in the longitudinal plane. Homogeneous and two fluid multiphase models are used to predict the natural and the ventilated supercavitating flows. In the fixed frequency pitching motions, a variety of working conditions are considered, including the pitching angular velocities and the supercavity scales and the results are found to be consistent with the available experimental results in literature. The mesh deformation technology controlled by the moment of momentum equation is adopted to study the free pitching motions and finally to obtain the planing states proposed by Savchenko. The numerical method is validated for predicting the pitching motions of supercavitating vehicles and is found to enjoy better calculation efficiency as comparing with the mesh regeneration technology.

Control System of Moving Target Simulator

To test the accuracy of image motion compensation of space camera, the moving target simulator was developed according to the principle of relative motion. As the core controller, PIC microcontroller controls DC motor to drive photoetching turntable rotating to simulate the relative linear velocity between ground target and aircraft, and the rotation motion is divided into uniform velocity rotation and sinusoidal velocity rotation. Furthermore, the simulation of drift angle of aircraft was realized by controlling stepper motor to drive the photoetching turntable deflecting, and the deflection includes uniform deflection, sinusoidal velocity deflection and specified angle positioning. The design of the hardware and software of control system has been completed and tested, and the experiment results show that the control system has high control precision and meets the design requirements.

Stereokinetic phenomena revisited: The oscillating tilted bar, the swinging gate and the vertical contracting bar

We present here a revised version of our mathematical modelling of the stereokinetic phenomena known as the “oscillating tilted bar”, the “swinging gate” and the stereokinetic phenomenon elicited by a vertical, periodically contracting line segment simultaneously undergoing a lateral displacement from left to right and conversely in the frontal plane of an observer. The criticisms of Liu, Z. [(2004). On the minimal relative motion principle—The oscillating tilted bar. Journal of Mathematical Psychology, 48, 196–198] and Rokers and Liu [(2004). On the minimal relative motion principle—Lateral displacement of a contracting bar. Journal of Mathematical Psychology, 48, 292–295.] helped us in reformulating our models, eliminating discrepancies and ambiguities. Characteristic of the present modelling is the clear definition of a multi-stage mathematical procedure matching different requirements posed by the Visual System, as we know them from our experimental observations.

The universal forms of the dynamic equations of holonomic mechanical system in relative motion

Based on the dynamic equations of particles system in non-inertial coordinate system, the higher order differential variational principle of relative motion for mechanical system is obtained, and the energy of higher order relative velocity of the mechanical system is introduced, the different kinds of higher order dynamic equations of holonomic mechanical system in relative motion are derived, and an example is given to illustrate the application of the results.

On the minimal relative motion principle—lateral displacement of a contracting bar

Xausa, Beghi, and Zanforlin (J. Math. Psychol. 45(4) (2001) 635) provide an account of perceptual organization based on their ‘minimal relative motion’ principle. They claim that this principle can account for the percept generated by a contracting bar that is simultaneously translating laterally. We critique the mathematical analysis provided in the aforementioned paper. We conclude that the ‘minimal relative motion’ principle, in the form presented, cannot adequately explain the percept reported by observers.

On the minimal relative motion principle—the oscillating tilted bar

Beghi, Xausa, Tomat, and Zanforlin (J. Math. Psychol. 41(1997) 11) present a visual stereokinetic illusion. In the image plane, one end of an oblique bar moves horizontally back and forth, while the other end is stationary. Perceptually, this becomes a bar of a constant length rotating in depth around a vertical axis that passes through the stationary end of the bar. Beghi et al. (1997) provide a mathematical model of minimal relative motion to account for this percept. Here we show that the minimal relative motion principle cannot explain the perceptual phenomenon. Specifically, we raise two objections. (1) It is necessary to consider not only the length, but also the direction, of a vector when comparing vector fields. In fact, when directions are taken into consideration, Beghi et al.'s mathematical result diverges from their perceptual experimental result. (2) There is a mathematical inconsistency in Beghi et al. (1997): mixing absolute and relative velocities in their minimization is unwarranted, and does not lead to correct minimization.

Dynamic response with respect to base movement of spring frame supported cantilever simple beam with concentrated mass

In this paper, the principle of relative motion is used to investigate the dynamic response of a spring-frame-supported cantilever simple beam with concentrated mass. Both free vibration and forced vibration caused by the base movement are studied. The cantilever simple beam is discretized into a simple beam and a cantilever beam. Therefore, the general analytical solution of homogeneous beams with uniform cross-section can be used in each beam. The general analytical solution of the whole beam in terms of initial parameters is obtained. In the case of free vibration, the frequency equation can be obtained in an analytical form, and in the case of base movement, a final solution can also be obtained analytically by using the dynamic response of the supporting spring frame as its vibrating source. From our analysis one can see that the accuracy of the solution of the spring-mass of two degrees of freedom is quite satisfactory for engineering purposes in the case of considering only the movement of the point where the concentrated mass P stands.

A Method for Increasing the Safe Power Input of X-Ray Tubes

A method for cooling x-ray tubes was devised, based on the principle of relative motion between the target and focal spot. The electron beam is deflected by a rotating magnetic field so that the focal spot moves in a circle upon the target face. Simultaneously, the tube itself is gyrated (without rotation about its axis) so that any point on the target describes an equal circle. The two rotations are equal in frequency but phased 180 degrees from each other. Thus the focal spot remains stationary in laboratory space. The advantages are (1) it is adaptable to most x-ray tubes with target face perpendicular to the tube axis, and target diameter twice that of the longest focal spot dimension, without any modification of tube design; (2) it combines the benefits of a rotating target, water-cooled target, and line focus without the need for rotating joints or vacuum connections. Tubes, operating continuously for hours at a time at a gyrating frequency of 6 r.p.s. have been cooled successfully by this method without observable shifting of the focal spot in laboratory space.

The Wind Channel: Its Design and Use

It has long been realised that experiments in the laboratory on small models afford in certain cases a means of obtaining, cheaply and rapidly, information on the behaviour of the actual structure under the conditions in which it is to be used. This plan has been adopted in many branches of science, and in none to a larger extent than in naval and aeronautical architecture. The problems to be investigated are usually those connected with the motion of bodies through a fluid, but if we accept the principle of relative motion we have an alternative method open to us for our model experiments. We may, if we wish, reverse the conditions and set the fluid in motion, the model remaining stationary. Generally speaking, one plan has been adopted in naval architecture and the other in aeronautics. In the former case models are towed through water in a ship tank, while in the latter they are placed in a tube through which air is passed.