Dynamics of a Rotor-Pendulum With a Small, Stiff Propeller in Wind

2016 ◽  
Author(s):  
William Craig ◽  
Derrick Yeo ◽  
Derek A. Paley
Keyword(s):  
System Dynamics ◽  
Equations Of Motion ◽  
Test Stand ◽  
Stable System ◽  
New Applications ◽  
Gust Response

As small rotorcraft grow in capability, the possibilities for their application increase dramatically. Many of these new applications require stable outdoor flight, necessitating a closer look at the aerodynamic response of the aircraft in windy environments. This paper develops the equations of motion for a single-propeller test stand by analyzing the blade-flapping response of a small-stiff propeller in wind. The system dynamics are simulated to show behavior under various wind conditions, and stable system equilibria are identified. Experiments with a rotor-pendulum validate the simulations, including system equilibria and gust response.

A Unified Framework for Dynamics and Lyapunov Stability of Holonomically Constrained Rigid Bodies

2005 ◽  
Vol 9 (4) ◽  
pp. 387-394 ◽  
Author(s):  
Khoder Melhem ◽  
◽  
Zhaoheng Liu ◽  
Antonio Loría ◽  
◽  
...  
Keyword(s):  
System Dynamics ◽  
Lyapunov Stability ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Minimal Realization ◽  
State Variables ◽  
Unified Framework ◽  
Constrained System ◽  
And Control

A new dynamic model for interconnected rigid bodies is proposed here. The model formulation makes it possible to treat any physical system with finite number of degrees of freedom in a unified framework. This new model is a nonminimal realization of the system dynamics since it contains more state variables than is needed. A useful discussion shows how the dimension of the state of this model can be reduced by eliminating the redundancy in the equations of motion, thus obtaining the minimal realization of the system dynamics. With this formulation, we can for the first time explicitly determine the equations of the constraints between the elements of the mechanical system corresponding to the interconnected rigid bodies in question. One of the advantages coming with this model is that we can use it to demonstrate that Lyapunov stability and control structure for the constrained system can be deducted by projection in the submanifold of movement from appropriate Lyapunov stability and stabilizing control of the corresponding unconstrained system. This procedure is tested by some simulations using the model of two-link planar robot.

The Automatic Stabilization Algorithm for Euler-Lagrange Equations With Holonomic/Nonholonomic Constraints in Multibody System Dynamics

2001 ◽  
Author(s):  
Zhenkuan Pan ◽  
Weijia Zhao
Keyword(s):  
System Dynamics ◽  
Multibody System ◽  
Equations Of Motion ◽  
Nonholonomic Constraints ◽  
Multibody System Dynamics ◽  
Integration Step ◽  
Lagrange Equations ◽  
Constraint Violation ◽  
Automatic Stabilization ◽  
The One

Abstract A new automatic constraint violation stabilization algorithm for numerical integration of Euler-Lagrange equations of motion of multibody system dynamics based on Baumgarte constraint violation stabilization method and Taylor expansion of constraint functions is presented. The constraint equations may be holonomic or nonholonomic. The parameters α, β, σ used in Baumgarte’s method are determined automatically according to integration step. Some numerical examples compare the accuracy between the traditional method and the one suggested in this paper are presented finally.

Open-Loop Nonlinear Vibration Control of Shallow Arches via Perturbation Approach

2002 ◽  
Vol 69 (3) ◽  
pp. 325-334 ◽  
Author(s):  
W. Lacarbonara ◽  
C.-M. Chin ◽  
R. R. Soper
Keyword(s):  
System Dynamics ◽  
Parametric Resonance ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Numerical Approach ◽  
Open Loop ◽  
Perturbation Approach ◽  
Nonlinear Controller ◽  
Beneficial Effects ◽  
Control Authority

An open-loop nonlinear control strategy applied to a hinged-hinged shallow arch, subjected to a longitudinal end-displacement with frequency twice the frequency of the second mode (principal parametric resonance), is developed. The control action—a transverse point force at the midspan—is typical of many single-input control systems; the control authority onto part of the system dynamics is high whereas the control authority onto some other part of the system dynamics is zero within the linear regime. However, although the action of the controller is orthogonal, in a linear sense, to the externally excited first antisymmetric mode, beneficial effects are exerted through nonlinear actuator action due to the system structural nonlinearities. The employed mechanism generating the effective nonlinear controller action is a one-half subharmonic resonance (control frequency being twice the frequency of the excited mode). The appropriate form of the control signal and associated phase is suggested by the dynamics at reduced orders, determined by a multiple-scales perturbation analysis directly applied to the integral-partial-differential equations of motion and boundary conditions. For optimal control phase and gain—the latter obtained via a combined analytical and numerical approach with minimization of a suitable cost functional—the parametric resonance is cancelled and the response of the system is reduced by orders of magnitude near resonance. The robustness of the proposed control methodology with respect to phase and frequency variations is also demonstrated.

Analysis of equations of motion for second-order systems using generalized velocity components

2007 ◽  
Vol 221 (2) ◽  
pp. 205-212 ◽  
Author(s):  
P Herman
Keyword(s):  
Differential Equations ◽  
System Dynamics ◽  
Equations Of Motion ◽  
Second Order ◽  
Model Based ◽  
Interesting Insight ◽  
Disturbance Model ◽  
Second Order Systems ◽  
Multi Body ◽  
Insight Into

An analysis of equations of motion expressed in terms of generalized velocity components (GVCs) for two second-order systems is presented in this paper. The two-link planar manipulator and the cart-pendulum are considered. It was shown that using GVC, two firstorder differential equations are obtained, which give some useful information about the system. The analysis allows one to detect several interesting properties concerning the system. In addition, A friction or disturbance model based on GVC can be considered, which gives an interesting insight into the system dynamics. The results of the analysis can be extended to multi-body systems.

Modeling Tribological Impact on Overall System Dynamics

2005 ◽  
Author(s):  
Pradeep K. Gupta
Keyword(s):  
System Dynamics ◽  
System Performance ◽  
Dynamic Performance ◽  
Equations Of Motion ◽  
Operating Conditions ◽  
Material Behavior ◽  
Equilibrium Analysis ◽  
System Component ◽  
And Performance ◽  
Dynamics Models

While the support bearings are key elements of rotating machinery systems, the overall system performance and design depend on a close integration of several disciplines. For prescribed life and operating environment the applied static loads and speeds on each of the system component may be generally determined by an equilibrium analysis. Conventional rotor dynamics models may be used to model overall system dynamics, rotor response and dynamic loads imposed on the support bearings. As a function of these applied conditions bearing response and dynamic performance is determined by integration of the equations of motion of each bearing element; in the case of rolling bearings, the available bearing dynamics models, such as ADORE (Advanced Dynamics Of Rolling Elements) provide integration of the classical differential equations of motion to model real-time performance of the bearing. With prescribed bearing geometry and applied operating conditions, it is well established that lubricant properties and mechanics play a major role in determining the stability of bearing elements and overall system performance. The rolling-sliding interactions in the concentrated contacts between the bearing elements produce heat, which travels through the bearing and the overall system. This affects temperature of the bearing elements, which in turn changes the bearing geometry and material behavior including the lubricant. Thus overall system design and performance simulation requires a close iteration between the various models at varying levels of sophistication.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

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