A New Method for Modeling of Fully Flexible Aircrafts

2011 ◽  
Vol 383-390 ◽  
pp. 2350-2355
Author(s):  
Dong Guo ◽  
Min Xu ◽  
Shi Lu Chen ◽  
Yu Qian
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Structural Model ◽  
Equations Of Motion ◽  
Flight Mechanics ◽  
Lagrangian Mechanics ◽  
Seamless Integration ◽  
Different Types ◽  
New Formulation ◽  
Nonlinear Rigid

The purpose of this study is to produce a modeling capability for integrated flight dynamics of flexible aircraft that can better predict some of the complex behaviors in flight due to multi-physics coupling. Based on the studying of the exiting modeling approaches, the author put forward a new modeling method, and developed a new formulation integrating nonlinear rigid-body flight mechanics and linear aeroelastic dynamics for fully elastic aircrafts using Lagrangian mechanics. The new equations of motion overcome the disadvantages of the exiting methods, and include automatically all six rigid-body degrees of freedom and elastic information, the seamless integration is achieved by using the same reference frame and the same variables to describe the aircraft motions and the forces acting on it, including the aerodynamic forces. The formulation is modular in nature, in the sense that the structural model, the aerodynamic theory, and the controls method can be replaced by any other ones to better suit different types of aircraft.

A Hybrid Highly Parallelizable Algorithm for the Dynamics of Rigid Body Chain Systems

1999 ◽  
Author(s):  
Shanzhong Duan ◽  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Constraint Forces ◽  
Dynamics Of Rigid Body ◽  
A Chain ◽  
Explicit Determination ◽  
Order Algorithm

Abstract The paper presents a new hybrid parallelizable low order algorithm for modeling the dynamic behavior of multi-rigid-body chain systems. The method is based on cutting certain system interbody joints so that largely independent multibody subchain systems are formed. These subchains interact with one another through associated unknown constraint forces f¯c at the cut joints. The increased parallelism is obtainable through cutting the joints and the explicit determination of associated constraint loads combined with a sequential O(n) procedure. In other words, sequential O(n) procedures are performed to form and solve equations of motion within subchains and parallel strategies are used to form and solve constraint equations between subchains in parallel. The algorithm can easily accommodate the available number of processors while maintaining high efficiency. An O[(n+m)Np+m(1+γ)Np+mγlog2Np](0<γ<1) performance will be achieved with Np processors for a chain system with n degrees of freedom and m constraints due to cutting of interbody joints.

scholarly journals The Dynamical Behavior of a Rigid Body Relative Equilibrium Position

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
T. S. Amer
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Relative Equilibrium ◽  
Dynamical Behavior ◽  
Vertical Plane ◽  
The Body ◽  
Physical Parameters ◽  
Pendulum Model

In this paper, we will focus on the dynamical behavior of a rigid body suspended on an elastic spring as a pendulum model with three degrees of freedom. It is assumed that the body moves in a rotating vertical plane uniformly with an arbitrary angular velocity. The relative periodic motions of this model are considered. The governing equations of motion are obtained using Lagrange’s equations and represent a nonlinear system of second-order differential equations that can be solved in terms of generalized coordinates. The numerical solutions are investigated using the fourth-order Runge-Kutta algorithms through Matlab packages. These solutions are represented graphically in order to describe and discuss the behavior of the body at any instant for different values of the physical parameters of the body. The obtained results have been discussed and compared with some previous published works. Some concluding remarks have been presented at the end of this work. The importance of this work is due to its numerous applications in life such as the vibrations that occur in buildings and structures.

scholarly journals New Aspects Concerning Dynamics of Rigid Solid Body in Plane-Parallel Motion Subjected to Real Constraints. Part One

2019 ◽  
Vol 24 (2) ◽  
pp. 175-180
Author(s):  
Vladimir Dragoş Tătaru ◽  
Mircea Bogdan Tătaru
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Dynamic Analysis ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Original Method ◽  
Horizontal Force ◽  
Constraint Forces ◽  
Inclined Plane ◽  
Parallel Motion

Abstract The present paper approaches in an original manner the dynamic analysis of a wheel which climbs on an inclined plane under the action of a horizontal force. The wheel rolls and slides in the same time. The two movements, rolling and sliding are considered to be independent of each other. Therefore we are dealing with a solid rigid body with two degrees of freedom. The difficulty of approaching the problem lies in the fact that in the differential equations describing the motion of the solid rigid body are also present the constraint forces and these are unknown. For this reason they must be eliminated from the differential equations of motion. The paper presents as well an original method of the constraint forces elimination.

Dynamic Contribution of Tires in Vehicle Suspension Modeling: An Experimental Approach

2003 ◽  
Author(s):  
Giuseppe Catania ◽  
Alessandro Zanarini
Keyword(s):  
Degrees Of Freedom ◽  
Experimental Approach ◽  
Structural Model ◽  
Equations Of Motion ◽  
Operating Conditions ◽  
Vehicle Suspension ◽  
Frequency Range ◽  
Full System ◽  
Linear Complex ◽  
Modal Model

An analytical-experimental approach is followed to obtain the dynamic model of a car vehicle, taking into account the full dynamic contribution due to tires. Linearized and condensed vehicle equations of motion are first introduced. The experimental modal model of a car tire, consisting of limited sets of eigenfrequencies and eigenshapes is then experimentally estimated in the frequency range Δftire=0÷300 Hz, starting from a restricted set of experimental degrees of freedom (d.o.f.). The tire is locally loaded to simulate the displacements due to gravitational loads and road contact occurring in operating conditions. Elastic coupling between the car structural model and the tire modal model is thus obtained; a linear, complex eigenproblem is thus formulated, and eigenfrequencies related to the full system are obtained as well. Results are reported and discussed in detail.

SYMBOLIC EQUATIONS FOR A FULL-CAR MODEL

2000 ◽  
Vol 24 (3-4) ◽  
pp. 493-514
Author(s):  
Natalie Baddour ◽  
K. A. Morris
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
A Priori ◽  
Active Suspension ◽  
Lagrangian Mechanics ◽  
Full Generality ◽  
Active Suspensions ◽  
Car Model ◽  
Simplifying Assumptions ◽  
Improved Performance

Active suspensions provide improved performance over conventional, passive suspensions. In this paper, modelling issues for an active suspension are considered. Symbolic equations for a full car model are derived using Lagrangian mechanics. The model has ten degrees of freedom instead of the usual seven. Furthermore, many of the usual simplifying assumptions are not made a priori so that the model retains its full generality. The model is developed so that modifications to any of the assumptions might easily be made and so that the equations of motion can be easily altered to satisfy more restrictive assumptions.

Rigid Body dynamics and decoupled control architecture for two strongly interacting manipulators

Robotica ◽  
1991 ◽  
Vol 9 (4) ◽  
pp. 421-430 ◽  
Author(s):  
M.A. Unseren
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Position Control ◽  
Equations Of Motion ◽  
Joint Space ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Control Architecture ◽  
Reduced Order ◽  
Closed Chain

SUMMARYA rigid body dynamical model and control architecture are developed for the closed chain motion of two structurally dissimilar manipulators holding a rigid object in a three-dimensional workspace. The model is first developed in the joint space and then transformed to obtain reduced order equations of motion and a separate set of equations describing the behavior of the generalized contact forces. The problem of solving the joint space and reduced order models for the unknown variables is discussed. A new control architecture consisting of the sum of the outputs of a primary and secondary controller is suggested which, according to the model, decouples the force and position-controlled degrees of freedom during motion of the system. The proposed composite controller enables the designer to develop independent, non-interacting control laws for the force and position control of the complex closed chain system.

Designing Efficient Trajectories for Underwater Vehicles Using Geometric Control Theory

2005 ◽  
Author(s):  
M. Chyba ◽  
T. Haberkorn
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Underwater Vehicles ◽  
Lagrangian Mechanics ◽  
The Maximum Principle ◽  
Marine Vehicles ◽  
Time Problem ◽  
Time Optimal ◽  
6 Degrees Of Freedom ◽  
Minimum Time Problem

In this paper, we consider the minimum time problem for underwater vehicles. Using Lagrangian mechanics, we write the equations of motion for marine vehicles with 6 degrees of freedom as a controlled mechanical system. We then apply the necessary conditions from the maximum principle for a trajectory to be time optimal. Using techniques from differential geometry we analyze the resuls. Finally we supplement the theoretical study with numerical simulations.

scholarly journals The Motion of a Rigid Body in the Presence of a Gyrostatic : الحركات المغزلية السريعة لجسم متماسك في مجال قوة نيوتوني في حالة وجود العزم

2019 ◽  
Vol 3 (1) ◽  
Author(s):  
Ghadir Ahmed Sahli
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
First Integral ◽  
Geometric Interpretation ◽  
The Body ◽  
Parameter Method ◽  
Principal Axes ◽  
Linear Autonomous System ◽  
Newtonian Force Field

In this study، the rotational motion of a rigid body about a fixed point in the Newtonian force field with a gyrostatic momentum  about the z-axis is considered. The equations of motion and their first integrals are obtained and reduced to a quasi-linear autonomous system with two degrees of freedom with one first integral. Poincare's small parameter method is applied to investigate the analytical peri­odic solutions of the equations of motion of the body with one point fixed، rapidly spinning about one of the principal axes of the ellipsoid of inertia. A geometric interpretation of motion is given by using Euler's angles to describe the orientation of the body at any instant of time.

Some Extensions of the Classical Approach to Strip Theory of Ship Motions, Including the Calculation of Mean Added Forces and Moments

1978 ◽  
Vol 22 (01) ◽  
pp. 1-19 ◽  
Author(s):  
Theodore A. Loukakis ◽  
Paul D. Scfavounos
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Dynamical Theory ◽  
Forced Oscillations ◽  
Ship Motions ◽  
Regular Waves ◽  
Strip Theory ◽  
Calm Water ◽  
Exciting Forces ◽  
New Formulation

The application of the dynamical theory to the problem of a ship moving with constant forward speed on a free surface has been extended to include the exciting forces in oblique regular waves. As a result, it has become possible to derive a new formulation for the equations of motion, for a ship moving with five degrees of freedom. The application of the same theory has yielded formulas for the calculation of the mean added resistance and drift force in oblique regular waves and the calculation of all mean forces and moments for the forced oscillations of a ship in calm water.

Augmented Perpetual Manifolds and Perpetual Mechanical Systems-Part I: Definitions, Theorem and Corollary for Triggering Perpetual Manifolds, Application in Reduced Order Modeling and Particle-Wave Motion of Flexible Mechanical Systems

2021 ◽  
Author(s):  
Fotios Georgiades
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Mechanical Engineering ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Reduced Order ◽  
Rigid Body Motions ◽  
Definition Of ◽  
External Forces ◽  
Perpetual Points

Abstract Perpetual points in mechanical systems defined recently. Herein are used to seek specific types of solutions of N-degrees of freedom systems, and their significance in mechanics is discussed. In discrete linear mechanical systems, is proven, that the perpetual points are forming the perpetual manifolds and they are associated with rigid body motions, and these systems are called perpetual. The definition of perpetual manifolds herein is extended to the augmented perpetual manifolds. A theorem, defining the conditions of the external forces applied in an N-degrees of freedom system lead to a solution in the exact augmented perpetual manifold of rigid body motions, is proven. In this case, the motion by only one differential equation is described, therefore forms reduced-order modelling of the original equations of motion. Further on, a corollary is proven, that in the augmented perpetual manifolds for external harmonic force the system moves in dual mode as wave-particle. The developed theory is certified in three examples and the analytical solutions are in excellent agreement with the numerical simulations. The outcome of this research is significant in several sciences, in mathematics, in physics and in mechanical engineering. In mathematics, this theory is significant for deriving particular solutions of nonlinear systems of differential equations. In physics/mechanics, the existence of wave-particle motion of flexible mechanical systems is of substantial value. Finally in mechanical engineering, the theory in all mechanical structures can be applied, e.g. cars, aeroplanes, spaceships, boats etc. targeting only the rigid body motions.

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