The stability of the rotational motions of a solid body with a liquid cavity

1959 ◽  
Vol 23 (6) ◽  
pp. 1512-1524 ◽  
Author(s):  
V.V Rumiantsev
Keyword(s):  
Solid Body ◽  
Rotational Motions ◽  
The Stability

On Stability of a Nonlinear, Periodically Time Varying, Rotating Blade

2011 ◽  
Author(s):  
Fengxia Wang
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Multiple Time ◽  
Time Varying ◽  
Rotating Blade ◽  
Stability And Bifurcation ◽  
Geometric Stiffening ◽  
Rotational Motions ◽  
The Stability

This paper discusses the stability of a periodically time-varying, spinning blade with cubic geometric nonlinearity. The modal reduction method is adopted to simplify the nonlinear partial differential equations to the ordinary differential equations, and the geometric stiffening is approximated by the axial inertia membrane force. The method of multiple time scale is employed to study the steady state motions, the corresponding stability and bifurcation for such a periodically time-varying rotating blade. The backbone curves for steady-state motions are achieved, and the parameter map for stability and bifurcation is developed. Illustration of the steady-state motions is presented for an understanding of rotational motions of the rotating blade.

scholarly journals Solving a Problem of Rotary Motion for a Heavy Solid Using the Large Parameter Method

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
A. I. Ismail
Keyword(s):  
Angular Velocity ◽  
Small Parameter ◽  
Initial Conditions ◽  
Geometric Interpretation ◽  
Rigid Bodies ◽  
Parameter Method ◽  
Large Parameter ◽  
Small Parameter Method ◽  
Rotational Motions ◽  
The Stability

The small parameter method was applied for solving many rotational motions of heavy solids, rigid bodies, and gyroscopes for different problems which classify them according to certain initial conditions on moments of inertia and initial angular velocity components. For achieving the small parameter method, the authors have assumed that the initial angular velocity is sufficiently large. In this work, it is assumed that the initial angular velocity is sufficiently small to achieve the large parameter instead of the small one. In this manner, a lot of energy used for making the motion initially is saved. The obtained analytical periodic solutions are represented graphically using a computer program to show the geometric periodicity of the obtained solutions in some interval of time. In the end, the geometric interpretation of the stability of a motion is given.

scholarly journals ON THE STABILITY OF PLANE MOVEMENT OF MOBILE ROBOTS

2020 ◽  
pp. 11-16
Author(s):  
E. S. Briskin ◽  
K. S. Artemyev ◽  
I. P. Vershinina ◽  
A. V. Maloletov
Keyword(s):  
Mobile Robots ◽  
Solid Body ◽  
Plane Motion ◽  
Force Action ◽  
The Stability ◽  
Pushing And Pulling

The problem of stability of the plane motion of mobile robots, including those with walking propulsion devices, is considered. Two modes of propulsion devices are compared: "pushing" and "pulling". The solution of two model problems on the plane motion of a solid body caused by kinematic and force action is presented.

The Stability of Aeroplanes

1914 ◽  
Vol 18 (70) ◽  
pp. 68-85
Author(s):  
Leonard Bairstow
Keyword(s):  
Solid Body ◽  
Vital Importance ◽  
The Subject ◽  
The Stability ◽  
Type Of Stability ◽  
Considerable Complexity ◽  
Naval Architect

The problems which arise in the course of a study of aeroplane stability are of considerable complexity as compared with those confronting engineers in other branches of locomotion. Ocean–going vessels provide another instance of the motion of a solid body in a fluid and their stability is clearly one of vital importance. Naval architects have consequently studied the subject and calculations are made for the stability of each new design of ship. The process is so well known and so well founded that it surprises no one that a newly launched vessel remains on an even keel. One instance, not connected with British shipbuilding, serves to remind designers of the serious consequences of faulty calculation. The disaster relates to a ship which was launched fully engined, etc., and which turned turtle and sank within a few minutes of launching. The type of stability which the naval architect needs to calculate most carefully is that which is concerned with the security of the ship when rolling.

scholarly journals Analysis of the Oscillating Motion of a Solid Body on Vibrating Bearers

Machines ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 58 ◽  
Author(s):  
Bissembayev ◽  
Jomartov ◽  
Tuleshov ◽  
Dikambay
Keyword(s):  
Solid Body ◽  
Quantitative Methods ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Horizontal Displacement ◽  
Oscillatory Process ◽  
Highly Nonlinear ◽  
Cumulative Curve ◽  
The Stability ◽  
Oscillating Motion

This article considers the oscillation of a solid body on kinematic foundations, the main elements of which are rolling bearers bounded by high-order surfaces of rotation at horizontal displacement of the foundation. Equations of motion of the vibro-protected body have been obtained. It is ascertained that the obtained equations of motion are highly nonlinear differential equations. Stationary and transitional modes of the oscillatory process of the system have been investigated. It is determined that several stationary regimes of the oscillatory process exist. Equations of motion have been investigated also by quantitative methods. In this paper the cumulative curves in the phase plane are plotted, a qualitative analysis for singular points and a study of them for stability are performed. In the Hayashi plane a cumulative curve of a body protected against vibration forms a closed path which does not tend to the stability of a singular point. This means that the vibration amplitude of a body protected against vibration does not remain constant in a steady state, but changes periodically.

scholarly journals Stability of stationary endwall boundary layers during spin-down

1996 ◽  
Vol 326 ◽  
pp. 373-398 ◽  
Author(s):  
J. M. Lopez ◽  
P. D. Weidman
Keyword(s):  
Boundary Layers ◽  
Solid Body ◽  
Experimental Studies ◽  
Steady Flows ◽  
Body Rotation ◽  
Solid Body Rotation ◽  
Centrifugal Instability ◽  
Self Similar ◽  
Layer Flow ◽  
The Stability

Since Bödewadt's (1940) seminal work on the boundary layer flow produced by a fluid in solid-body rotation over a stationary disk of infinite radius there has been much interest in determining the stability of such flows. To date, it appears that there is no theoretical study of the stability of Bödewadt's self-similar solution to perturbations that are not self-similar. Experimental studies have been compromised due to the difficulty in establishing these steady flows in the laboratory. Savaç (1983, 1987) has studied the endwall boundary layers of flow in a circular cylinder following impulsive spin-down. During the first few radians of rotation, the endwall boundary layers have a structure very similar to Bödewadt layers. For certain conditions, SavaÇ has observed a series of axisymmetric waves travelling radially inwards in the endwall boundary layers. The conjecture is that these waves represent a mode of instability of the Bödewadt layer. Within a few radians of rotation however, the centrifugal instability of the sidewall layer dominates the spin-down process and the endwall waves are difficult to examine further.Here, the impulsive spin-down problem is examined numerically for Savaç’ (1983, 1987) conditions and good agreement with his experiments is achieved. New experimental results are also presented, which include quantitative space-time information regarding the axisymmetric waves. These agree well with both the numerics and the earlier experimental work. Further, a related problem is considered numerically. This flow is also initially in solid-body rotation, but only the endwalls are impulsively stopped, keeping the sidewall rotating. This results in a flow virtually identical to the usual spin-down flow for the first few radians of rotation, except in the immediate vicinity of the sidewall. The sidewall layer is no longer centrifugally unstable and the circular waves on the endwalls are observed without the influence of the sidewall instability.

scholarly journals Asymptotic Stability of Quaternion-based Attitude Control System with Saturation Function

2017 ◽  
Vol 7 (4) ◽  
pp. 1994 ◽  
Author(s):  
Harry Septanto ◽  
Djoko Suprijanto
Keyword(s):  
Control System ◽  
Angular Velocity ◽  
Rigid Body ◽  
Attitude Control ◽  
Asymptotically Stable ◽  
Attitude Control System ◽  
Saturation Function ◽  
Continuous Scheme ◽  
Rotational Motions ◽  
The Stability

In the design of attitude control, rotational motion of the spacecraft is usually considered as a rotation of rigid body. Rotation matrix parameterization using quaternion can represent globally attitude of a rigid body rotational motions. However, the representation is not unique hence implies difficulties on the stability guarantee. This paper presents asymptotically stable analysis of a continuous scheme of quaternion-based control system that has saturation function. Simulations run show that the designed system applicable for a zero initial angular velocity case and a non-zero initial angular velocity case due to utilization of deadzone function as an element of the defined constraint in the stability analysis.

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