On the equations of motion for a heavy body with a fixed point

1963 ◽  
Vol 27 (4) ◽  
pp. 1070-1078 ◽  
Author(s):  
P.V Kharlamov
Keyword(s):  
Fixed Point ◽  
Equations Of Motion ◽  
Heavy Body

Transient motion of a dipole in a rotating flow

1969 ◽  
Vol 39 (3) ◽  
pp. 433-442 ◽  
Author(s):  
John W. Miles
Keyword(s):  
Fixed Point ◽  
Axial Velocity ◽  
Potential Flow ◽  
Equations Of Motion ◽  
Rotating Flow ◽  
Rossby Number ◽  
Laboratory Measurements ◽  
Transient Motion ◽  
Experimental Scatter ◽  
Upstream Waves

The question of whether or not waves exist upstream of an obstacle that moves uniformly through an unbounded, incompressible, inviscid, unseparated, rotating flow is addressed by considering the development of the disturbed flow induced by a weak, moving dipole that is introduced into an axisymmetric, rotating flow that is initially undisturbed. Starting from the linearized equations of motion, it is shown that the flow tends asymptotically to the steady flow determined on the hypothesis of no upstream waves and that the transient at a fixed point is O(1/t). It also is shown that the axial velocity upstream (x < 0) of the dipole as x → − ∞ with t fixed is O(|x|−3), as in potential flow, but is O(|x|−1) as t → ∞ with |x| fixed. The results extend directly to closed obstacles of sufficiently small transverse dimensions and suggest the existence of a finite, parametric domain of no upstream waves for smooth, slender obstacles. The axial velocity in front of a small, moving sphere at a given instant in the transient régime is calculated and compared with Pritchard's laboratory measurements. The agreement is within the experimental scatter for Rossby numbers greater than about 0·3 even though the equivalence between sphere and dipole is exact only for infinite Rossby number.

A Novel Method to Model the Dynamics of an Uniball Robot

2014 ◽  
Author(s):  
Pramod Chembrammel ◽  
Thenkurussi Kesavadas
Keyword(s):  
Fixed Point ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Euler Method ◽  
Kinematics And Dynamics ◽  
Euler Angles ◽  
Geometrical Center ◽  
Principal Moments Of Inertia ◽  
Geometrical Features ◽  
Novel Method

In this paper the kinematics and dynamics of a uniball robot is demonstrated. The motion of a uniball robot is derived from the dynamics of a sphere rolling on a surface which is considered as a motion about a fixed point. The equations of motion are derived using Newton-Euler method incorporating the geometrical features of the surface. A uniball-robot can be considered as a Routh’s sphere whose center of mass is not at the geometrical center and have equal principal moments of inertia in the plane perpendicular to the axis connecting the center of mass and the geometrical center. The Euler angles are obtained using the Meusnier’s theorem which deals with the evolution of the surface as the robot moves along.

On the motion of a liquid-filled heavy body around a fixed point

2017 ◽  
Vol 76 (1) ◽  
pp. 113-145 ◽  
Author(s):  
Giovanni P. Galdi ◽  
Giusy Mazzone ◽  
Mahdi Mohebbi
Keyword(s):  
Fixed Point ◽  
Heavy Body

scholarly journals An approach in studying gyrostat motion with variable gyrostatic moment

2021 ◽  
Vol 31 (1) ◽  
pp. 102-115
Author(s):  
G.V. Gorr
Keyword(s):  
Fixed Point ◽  
Explicit Form ◽  
Poisson Equation ◽  
Mass Distribution ◽  
Equations Of Motion ◽  
Order System ◽  
Constant Multiplier ◽  
The Poisson Equation ◽  
Spherical Mass ◽  
Fifth Order

The problem of the motion of a gyrostat with a fixed point and a variable gyrostatic moment under the action of gravity force is considered. A new method for integrating the equations of motion of a system consisting of a carrier body and three rotors that rotate around the main axes is proposed. The method can be attributed to the method of variation of the constant in the function for the gyrostatic moment, which linearly depends on the vector of vertical. In case of a constant multiplier, the gyrostatic moment satisfies the Poisson equation, and its variation is found from the integral of areas. The original equations have been reduced to a fifth-order system. New solutions of these equations are obtained in the case of a spherical mass distribution for the gyrostat and for the precessional motions of a carrier body. An explicit form of the gyrostatic moment is established for the case of three invariant relations.

scholarly journals Comments on contact terms and conformal manifolds in the AdS/CFT correspondence

2020 ◽  
Author(s):  
Tadakatsu Sakai ◽  
Masashi Zenkai
Keyword(s):  
Fixed Point ◽  
Correlation Functions ◽  
Equations Of Motion ◽  
Mathematical Structure ◽  
Regularization Scheme ◽  
Anomalous Dimensions ◽  
Geometrical Data ◽  
Conformal Manifolds ◽  
General Setup ◽  
Marginal Deformation

Abstract We study the contact terms that appear in the correlation functions of exactly marginal operators using the AdS/CFT correspondence. It is known that CFT with an exactly marginal deformation requires the existence of the contact terms is crucial for a consistency of with their coefficients having a geometrical interpretation in the context of conformal manifolds. We show that the AdS/CFT correspondence captures properly the mathematical structure of the correlation functions that is expected from the CFT analysis. For this purpose, we employ holographic RG to formulate a most general setup in the bulk for describing an exactly marginal deformation. The resultant bulk equations of motion are nonlinear and solved perturbatively to obtain the on-shell action. We compute three- and four-point functions of the exactly marginal operators using the GKP-Witten prescription, and show that they match with the expected results precisely. It is pointed out that The cut-off surface prescription in the bulk provides us with a regularization scheme for performing a conformal perturbation. serves as a regularization scheme for conformal perturbation theory in the boundary CFT. around a fixed point is regularized by putting a cut-off surface in the bulk. As an application, we examine a double OPE limit of the four-point functions. The anomalous dimensions of double trace operators are written in terms of the geometrical data of a conformal manifold.

scholarly journals Applying the Large Parameter Technique for Solving a Slow Rotary Motion of a Disc about a Fixed Point

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
A. I. Ismail
Keyword(s):  
Fixed Point ◽  
Angular Velocity ◽  
Periodic Solutions ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Numerical Technique ◽  
Equations Of Motion ◽  
First Integral ◽  
The Body ◽  
Large Parameter

In this paper, the motion of a disk about a fixed point under the influence of a Newtonian force field and gravity one is considered. We modify the large parameter technique which is achieved by giving the body a sufficiently small angular velocity component r0 about the fixed z-axis of the disk. The periodic solutions of motion are obtained in the neighborhood r0 tends to 0. This case of study is excluded from the previous works because of the appearance of a singular point in the denominator of the obtained solutions. Euler-Poison equations of motion are obtained with their first integrals. These equations are reduced to a quasilinear autonomous system of two degrees of freedom and one first integral. The periodic solutions for this system are obtained under the new initial conditions. Computerizing the obtained periodic solutions through a numerical technique for validation of results is done. Two types of analytical and numerical solutions in the new domain of the angular velocity are obtained. Geometric interpretations of motion are presented to show the orientation of the body at any instant of time t.

Sign in / Sign up

Export Citation Format

Share Document