SEVERAL MODELS OF SIX DEGREE OF FREEDOM EQUATIONS OF MOTION FOR A BALLISTIC MISSILE

1962 ◽  
Author(s):  
R. A. Collins ◽  
W. A. Miller
Keyword(s):  
Equations Of Motion ◽  
Ballistic Missile ◽  
Degree Of Freedom ◽  
Six Degree Of Freedom

The Dynamics of Ball Bearings

1971 ◽  
Vol 93 (1) ◽  
pp. 1-10 ◽  
Author(s):  
C. T. Walters
Keyword(s):  
Fourth Order ◽  
Ball Bearing ◽  
Equations Of Motion ◽  
Numerical Results ◽  
Degree Of Freedom ◽  
Spin Axis ◽  
General Analysis ◽  
Ball Bearings ◽  
High Speeds ◽  
Six Degree Of Freedom

The details of the dynamics of the elements of a ball bearing become increasingly important at high speeds. A comprehensive general analysis of the motions of balls and a ball separator with realistic lubrication is summarized. The equations of motion consider four degree-of-freedom balls and a six degree-of-freedom separator and are integrated numerically with a fourth order Runge Kutta scheme. Numerical results are presented for a particular spin axis gyro bearing configuration.

scholarly journals Dynamics and vibration analysis of the interface between a non-rigid sphere and omnidirectional wheel actuators

Robotica ◽  
2014 ◽  
Vol 33 (9) ◽  
pp. 1850-1868 ◽  
Author(s):  
A. Weiss ◽  
R. G. Langlois ◽  
M. J. D. Hayes
Keyword(s):  
Rotational Motion ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Design Tool ◽  
Degree Of Freedom ◽  
Rigid Sphere ◽  
Motion Platform ◽  
Six Degree Of Freedom ◽  
Dynamics And Vibration ◽  
Omnidirectional Wheels

SUMMARYThis paper presents analysis of the dynamics and vibration of an orientation motion platform utilizing a sphere actuated by omnidirectional wheels. The purpose of the analysis is to serve as a design tool for the construction of a six-degree-of-freedom motion platform with unlimited rotational motion. The equations of motion are presented taking flexibility of the system into account. The behaviour of the system is illustrated by sample configurations with a range of omnidirectional wheel types and geometries. Vibration analysis follows, and sensitivity to various parameters is investigated. It is determined that the geometry of omnidirectional wheels has a significant effect on the behaviour of the system.

Application of Dual Quaternions to the Study of Gyrodynamics

1967 ◽  
Vol 89 (1) ◽  
pp. 137-143 ◽  
Author(s):  
A. T. Yang
Keyword(s):  
Equations Of Motion ◽  
Degree Of Freedom ◽  
System Dynamic ◽  
Dynamic Equations ◽  
Dual Quaternions ◽  
Special Cases ◽  
Six Degree Of Freedom

Dual quaternions are used to derive equations of motion for an offset unsymmetrical gyroscope. From the equations, in view of the general characteristics of this six-degree-of-freedom system, dynamic equations for a variety of gyroscopic and pendulous systems may be deduced as special cases. Examples are given for illustration.

Analysis of an Offset Unsymmetric Gyroscope With Oblique Rotor Using (3×3) Matrices With Dual-Number Elements

1969 ◽  
Vol 91 (3) ◽  
pp. 535-541 ◽  
Author(s):  
An Tzu Yang
Keyword(s):  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Spin Axis ◽  
Dynamic Equations ◽  
Gyroscopic System ◽  
Dual Number ◽  
System A ◽  
Six Degree Of Freedom ◽  
Special Case

Using 3 × 3 matrices of dual-number elements, dynamic equations are obtained for an offset unsymmetric gyroscope with obliquely placed rotor, a generalized six-degree-of-freedom gyroscopic system (shown schematically in Fig. 3). Equations of motion for a special case of the system, a two-frame symmetric gyroscope, conventional in all aspects except the rotor is inclined relative to its spin axis, are deduced; these equations are applied to the study of the effects of a slightly inclined rotor on (a) a two-frame symmetric gyroscope in steady precession and (b) a Faucualt’s gyrocompass.

Calculation of Dynamic Tire Forces from Aircraft Instrumentation Data

2010 ◽  
Vol 38 (3) ◽  
pp. 182-193 ◽  
Author(s):  
Gary E. McKay
Keyword(s):  
System Performance ◽  
Equations Of Motion ◽  
Test Laboratory ◽  
Excellent Correlation ◽  
Friction Behavior ◽  
Aircraft Landing ◽  
Data Scatter ◽  
Tire Forces ◽  
Six Degree Of Freedom ◽  
Tire Friction

Abstract When evaluating aircraft brake control system performance, it is difficult to overstate the importance of understanding dynamic tire forces—especially those related to tire friction behavior. As important as they are, however, these dynamic tire forces cannot be easily or reliably measured. To fill this need, an analytical approach has been developed to determine instantaneous tire forces during aircraft landing, braking and taxi operations. The approach involves using aircraft instrumentation data to determine forces (other than tire forces), moments, and accelerations acting on the aircraft. Inserting these values into the aircraft’s six degree-of-freedom equations-of-motion allows solution for the tire forces. While there are significant challenges associated with this approach, results to date have exceeded expectations in terms of fidelity, consistency, and data scatter. The results show excellent correlation to tests conducted in a tire test laboratory. And, while the results generally follow accepted tire friction theories, there are noteworthy differences.

Iterative feedback control based on frequency response model for a six-degree-of-freedom micro-vibration platform

2021 ◽  
pp. 107754632199731
Author(s):  
He Zhu ◽  
Shuai He ◽  
Zhenbang Xu ◽  
XiaoMing Wang ◽  
Chao Qin ◽  
...  
Keyword(s):  
Feedback Control ◽  
Frequency Response ◽  
Control Strategy ◽  
Degree Of Freedom ◽  
Small Displacement ◽  
Response Model ◽  
Parameter Uncertainties ◽  
Micro Vibration ◽  
Six Degree Of Freedom ◽  
Iterative Feedback

In this article, a six-degree-of-freedom (6-DOF) micro-vibration platform (6-MVP) based on the Gough–Stewart configuration is designed to reproduce the 6-DOF micro-vibration that occurs at the installation surfaces of sensitive space-based instruments such as large space optical loads and laser communications equipment. The platform’s dynamic model is simplified because of the small displacement characteristics of micro-vibrations. By considering the multifrequency line spectrum characteristics of micro-vibrations and the parameter uncertainties, an iterative feedback control strategy based on a frequency response model is designed, and the effectiveness of the proposed control strategy is verified by performing integrated simulations. Finally, micro-vibration experiments are performed with a 10 kg load on the platform. The results of these micro-vibration experiments show that after several iterations, the amplitude control errors are less than 3% and the phase control errors are less than 1°. The control strategy presented in this article offers the advantages of a simple algorithm and high precision and it can also be used to control other similar micro-vibration platforms.

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