scholarly journals An Efficient Modeling of Flexible Blimps: Eulerian Approach

2007 ◽  
Author(s):  
Selima Bennaceur ◽  
Naoufel Azouz ◽  
Azgal Abichou
Keyword(s):  
Dynamical System ◽  
Rigid Body ◽  
Flight Control ◽  
Degrees Of Freedom ◽  
Body Motion ◽  
Lagrange Equations ◽  
Rigid Objects ◽  
The University ◽  
Surrounding Fluid ◽  
Efficient Modeling

Unmanned Aerial Vehicles (U.A.V.) have a need of a greater autonomy in their new missions. Autonomous U.A.V. flight control systems require a precise modeling of the dynamic behavior taking into account the effect of the flexibility and the interaction with the surrounding fluid. In this paper, we present an efficient modeling of the autonomous flexible blimps. These flying objects are assumed to undergo large rigid-body motion and small elastic deformations. The formalism used is based on the Newton-Euler approach. This one is frequently used for flying rigid objects. In this study we develop a method to generalize the existing Newton-Euler “rigid body” formalisms by including the effect of the flexibility without destroying the global methodology. The method is hybrid. It uses the Lagrange equations and the Eulerian variables. The flexibility appears in the global dynamical system by the way of few supplementary degrees of freedom. This method has the advantage of making easier the elaboration of algorithms of control, stabilization or generation of trajectories. The added mass phenomenon is also taken into account in the dynamical system. This phenomenon is important for big and light objects moving in a fluid such as airships. As validation we use the parameters of an AS-200 blimp belonging to the University of Evry.

scholarly journals Application of the dynamic Lorentz model to modeling the motion of a rigid body

2021 ◽  
pp. 32-36
Author(s):  
Nikolay Makeyev ◽  
Keyword(s):  
Dynamical System ◽  
Qualitative Research ◽  
Rigid Body ◽  
Body Motion ◽  
Dynamic Equations ◽  
Lorentz Model ◽  
Dissipative Forces ◽  
System Parameters ◽  
Phase Trajectories ◽  
Inertia Forces

A qualitative research of the field of phase trajectories of the system of dynamic equations of an absolutely rigid body was carried out, moving around the selected pole under the influence of gyroscopic, dissipative forces and Coriolis inertia forces. The equations of body motion are reduced to a dynamical system generating a Lorentz attractor. Under parametric constraints imposed on the equations of a dynamical system, the structure of its phase trajectories is described depending on the values of the system parameters.

Modeling the Dynamics of Five-Axis Machine Tool Using the Multibody Approach

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Hoai Nam Huynh ◽  
Yusuf Altintas
Keyword(s):  
Rigid Body ◽  
Machine Tool ◽  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Dynamic Performance ◽  
Body Motion ◽  
Proposed Model ◽  
Multibody Dynamic ◽  
Machining Operations ◽  
Five Axis

Abstract A systematic modeling of multibody dynamics of five-axis machine tools is presented in this article. The machine is divided into major subassemblies such as spindle, column, bed, tool changer, and longitudinal and rotary drives. The inertias and mass center of each subassembly are calculated from the design model. The subassemblies are connected with elastic springs and damping elements at contact joints to form the complete multibody dynamic model of the machine that considers the rigid body kinematics and structural vibrations of the machine at any point. The unknown elastic joint parameters are estimated from the experimental modal analysis of the machine tool. The resulting position-dependent multibody dynamic model has the minimal number of degrees-of-freedom that is equivalent to the number of measured modes, as opposed to thousands used in finite element models. The frequency response functions of the machine can be predicted at any posture of the five-axis machine, which are compared against the directly measured values to assess the validity of model. The proposed model can predict the combined rigid body motion and vibrations of the machine with computational efficiency, and hence, it can be used as a digital twin to simulate its dynamic performance in machining operations and tracking control tests of the servo drives.

scholarly journals Modeling Legged Microrobot Locomotion Based on Contact Dynamics and Vibration in Multiple Modes and Axes

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Jinhong Qu ◽  
Clark B. Teeple ◽  
Kenn R. Oldham
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Beam Theory ◽  
Contact Dynamics ◽  
Body Motion ◽  
Small Scale ◽  
Robot Locomotion ◽  
Actuation Scheme ◽  
Dynamics And Vibration

A dynamic model is developed for small-scale robots with multiple high-frequency actuated compliant elastic legs and a rigid body. The motion of the small-scale robots results from dual-direction motion of piezoelectric actuators attached to the legs, with impact dynamics increasing robot locomotion complexity. A dynamic model is developed to describe the small-scale robot motion in the presence of variable properties of the underlying terrain. The dynamic model is derived from beam theory with appropriate boundary and loading conditions and considers each robot leg as a continuous structure moving in two directions. Robot body motion is modeled in up to five degrees-of-freedom (DOF) using a rigid body approximation for the central robot chassis. Individual modes of the resulting multimode robot are treated as second-order linear systems. The dynamic model is tested with two different centimeter-scale robot prototypes having an analogous actuation scheme to millimeter-scale microrobots. In accounting for the interaction between the robot and ground, a dynamic model using the first two modes of each leg shows good agreement with experimental results for the centimeter-scale prototypes, in terms of both magnitude and the trends in robot locomotion with respect to actuation conditions.

Dynamic Analysis of Flexible Supercavitating Vehicles Using Modal Based Elements

2003 ◽  
Author(s):  
Jou-Young Choi ◽  
Massimo Ruzzene ◽  
Olivier A. Bauchau
Keyword(s):  
Numerical Model ◽  
Rigid Body ◽  
Degrees Of Freedom ◽  
Structural Characteristics ◽  
Rigid Body Motion ◽  
Operating Conditions ◽  
Flight Mechanics ◽  
Body Motion ◽  
Supercavitating Vehicles ◽  
Elastic Modes

This presents a numerical model for the simulation of the flight mechanics behavior of flexible supercavitating vehicles. Supercavitating vehicles exploit supercavitation as a means to reduce drag and increase the underwater speed. In the proposed formulation, the vehicle’s rigid body motion is described by 6 degrees of freedom, which define pitch, yaw and roll motion and the displacement of the center of gravity with respect to a fixed inertial reference system. The forces applied to the vehicle include the control actions at the nose and at the fins, propulsion, gravity and cavity/vehicle periodic interactions associated to typical operating conditions. The elastic displacements are superimposed to the rigid body motion through a modal superposition technique. The mode synthesis is performed using Herting’s Transformation, which provides maximum flexibility in the selection of the elastic modes to be used for the used for the superposition, and the possibility of easily handling free-free modes. The developed numerical model predicts the dynamic response of the considered class of supercavitating vehicles resulting from assigned maneuvers. The analysis is motivated by the need of accurately modeling the structural characteristics of supercavitating vehicles in order to estimate vibrations in the structure and to envision and design systems that improve their guidance and control efficiency.

Calculations of non-linear waves generated by complex body motion

2000 ◽  
Vol 214 (6) ◽  
pp. 771-780 ◽  
Author(s):  
T Chen ◽  
A T Chwang
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Grid Method ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Promising Alternative ◽  
Potential Flows ◽  
Linear Waves ◽  
Non Linear ◽  
Marine Engineering

A structured and unstructured hybrid overlapping grid method is developed for simulating free-surface waves generated by submerged arbitrary bodies undergoing rigid body motion in multi-degrees of freedom. Exact boundary conditions are applied to the transient free and body surfaces. The accuracy, efficiency and generality of the present two-dimensional code for potential flows are validated by comparisons with available theories and experiments. Numerical experiments are reported in this paper to investigate the non-linear behaviour of waves due to the complex rigid body motion, in terms of wave patterns and the pressure distribution. Combining the best features of both grid systems for finite elements and finite differences, the present method provides a promising alternative in computational fluid dynamics for the design and analysis in marine engineering.

Dynamic Model of the Piston-Ring Assembly Using Curved Beam Finite Elements

2011 ◽  
Author(s):  
Mohannad Hakeem ◽  
Nabil G. Chalhoub ◽  
Peter Schihl
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Piston Ring ◽  
Translational Motion ◽  
Total Duration ◽  
Variable Structure ◽  
Body Motion ◽  
Curved Beam ◽  
Connecting Rod

A dynamic model for the crankshaft/connecting-rod/piston-assembly for a single cylinder engine is developed. The model considers the rigid body motion of the crank-slider mechanism including the piston secondary motions such as the piston-slap and piston-tilting. The formulation considers the ring to have three rigid body degrees of freedom in addition to its longitudinal and in-plane transverse deformations. The structural flexibility terms are approximated by using curved beam finite element method. The dynamic model has a variable structure whereby the number of degrees of freedom depends on the piston-liner and piston-ring interactions. Its formulation does not include frictional losses. The simulation results illustrate the piston secondary motions along with the ring tilting angles relative to the piston orientation for the total duration of the engine cycle. In addition, they exhibit the translational motion of the ring within the piston groove.

scholarly journals On the Hamel Coefficients and the Boltzmann–Hamel Equations for the Rigid Body

2021 ◽  
Vol 31 (2) ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Rigid Body ◽  
Nonholonomic Systems ◽  
Rigid Bodies ◽  
Body Motion ◽  
Floating Body ◽  
Lagrange Equations ◽  
Local Coordinates ◽  
Dynamics And Control ◽  
Boltzmann Hamel Equations ◽  
And Control

AbstractThe Boltzmann–Hamel (BH) equations are central in the dynamics and control of nonholonomic systems described in terms of quasi-velocities. The rigid body is a classical example of such systems, and it is well-known that the BH-equations are the Newton–Euler (NE) equations when described in terms of rigid body twists as quasi-velocities. It is further known that the NE-equations are the Euler–Poincaré, respectively, the reduced Euler–Lagrange equations on SE(3) when using body-fixed or spatial representation of rigid body twists. The connection between these equations are the Hamel coefficients, which are immediately identified as the structure constants of SE(3). However, an explicit coordinate-free derivation has not been presented in the literature. In this paper the Hamel coefficients for the rigid body are derived in a coordinate-free way without resorting to local coordinates describing the rigid body motion. The three most relevant choices of quasi-velocities (body-fixed, spatial, and hybrid representation of rigid body twists) are considered. The corresponding BH-equations are derived explicitly for the rotating and free floating body. Further, the Hamel equations for nonholonomically constrained rigid bodies are discussed, and demonstrated for the inhomogenous ball rolling on a plane.

scholarly journals On the transition from regular to chaotic behaviors in the two degrees of freedom dynamical system

2007 ◽  
Vol 29 (3) ◽  
pp. 353-374
Author(s):  
Nguyen Van Khang ◽  
Nguyen Hoang Duong
Keyword(s):  
Dynamical System ◽  
Differential Equations ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Dynamical Behavior ◽  
Control Parameters ◽  
Lagrange Equations ◽  
Chaotic Motions ◽  
Two Degrees Of Freedom

The main objective of the present paper is to study the transition from periodic regular mot ion to chaos in a two degrees of freedom dynamical system by changing control parameters. The nonlinear differential equations governing motion of the system are derived from the Lagrange equations. By use of the Poincare map, the dynamical behavior is identified based on numerical solutions of the ordinary differential equations. The Lyapunov exponent and the frequency spectrum are calculated to identify chaos. From numerical simulations, it is indicated that the periodic, quasi-periodic and chaotic motions occur in the considered system.

Instantaneous Center of Rotation in Pitch Response of a FPSO Submitted to Head Waves

2018 ◽  
Author(s):  
Daniel de Oliveira Costa ◽  
Antonio Carlos Fernandes ◽  
Joel Sena Sales Junior ◽  
Peyman Asgari
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Tracking System ◽  
The Body ◽  
Body Motion ◽  
Floating Body ◽  
Wave System ◽  
Center Of Rotation ◽  
Head Waves ◽  
Instantaneous Center

When under influence of an incident wave system, any floating body presents a general motion with all six degrees of freedom, unless it presents some kind of restrains on it. For a free moving body, the center of rotation will depend on the force distribution and might not coincide with its center of gravity. For long and slender floating structures, such as FPSO platforms, a small change in the center of Pitch rotation would result in significant change in the overall motions in its fore and aft regions. Therefore, it is of high importance to obtain a better understating of the instantaneous position of the body center of rotation in Heave and Pitch response. This paper investigates the position of the Instantaneous Center of Rotation in Pitch Response of a scaled down model of a FPSO platform under different regular wave conditions. The investigation uses basic kinematics equations for rigid body, defining the 6 degrees of freedom of the rigid body motion from a finite number of markers installed in the model. A high quality tracking system captures the markers positions in order to define the rigid body at each instant of time. For an initial approach, the study considers the response due to head waves seas with experimental validation.

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