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Articles 451 - 480 of 598

Full-Text Articles in Aerospace Engineering

Stability Of Three-Dimensional Compressible Boundary-Layers, Samarasingham Jeyasingham Apr 1999

Stability Of Three-Dimensional Compressible Boundary-Layers, Samarasingham Jeyasingham

Mechanical & Aerospace Engineering Theses & Dissertations

The failure repair process of a continuously operating device is studied in this research. Different cases that incorporate modeling of equipment deterioration, inspection, and maintenance for optimal maintenance policy are proposed. Markov processes are used to determine state probabilities, and the optimal value of the mean time to preventive maintenance is determined by maximizing the availability of the equipment with respect to the meantime preventive maintenance. The approach uses models that assume that equipment can fail due to both deterioration and random failures. Preventive maintenance can be performed from each working state to avoid deterioration failure. Economic effects are integrated …


Aeroelastic Load Alleviation Using Shunted Piezolectrics, Anna-Maria Rivas Mcgowan Apr 1999

Aeroelastic Load Alleviation Using Shunted Piezolectrics, Anna-Maria Rivas Mcgowan

Mechanical & Aerospace Engineering Theses & Dissertations

Several analytical and experimental studies clearly demonstrate that piezoelectric materials (piezoelectrics) can be used as actuators to actively control vibratory response including aeroelastic response. However, two important issues in using piezoelectrics as actuators for active control are: 1) the potentially large amount of power required to operate the actuators, and 2) the complexities involved with active control (added hardware, control law design and implementation). Active or passive damping augmentation using shunted piezoelectrics may provide a viable alternative. This approach requires only simple electrical circuitry and very little or no electrical power. Shunted piezoelectrics have been shown to provide an efficient …


Assessment Of A Higher Harmonic Control System For Minimizing Vibrations On A Dynamically Scaled Tiltrotor Model, David J. Piatak Apr 1999

Assessment Of A Higher Harmonic Control System For Minimizing Vibrations On A Dynamically Scaled Tiltrotor Model, David J. Piatak

Mechanical & Aerospace Engineering Theses & Dissertations

The performance of a higher harmonic control system called the Multipoint Adaptive Vibration Suppression System (MA VSS) at reducing 3/rev wing vibratory loads and fuselage vibrations on a dynamically-scaled tiltrotor model is presented. Previous wind tunnel tests on a semispan aeroelastic tiltrotor model have demonstrated the effectiveness of MAVSS for reducing wing vibratory loads using both an active flaperon and swashplate. The primary goal, however, of such a vibration suppression system is to reduce tiltrotor fuselage vibrations in order to improve passenger comfort. The present study addresses the reduction of both wing and fuselage vibrations using MA VSS active flaperons …


Studies Related To The Design Of A Magnetic Suspension And Balance System For An Ultra-High Reynolds Number Flow Facility, Oscar Magno Michael Gomeiz Jan 1999

Studies Related To The Design Of A Magnetic Suspension And Balance System For An Ultra-High Reynolds Number Flow Facility, Oscar Magno Michael Gomeiz

Mechanical & Aerospace Engineering Theses & Dissertations

The basic design principles for a magnetic suspension and balance system applied to the test section of an ultra-high Reynolds number facility are defined. The design of the cross-sectional area to be used in the test section is analyzed. The parameters of the permanent magnet to be used in the model inside the test section are investigated. The testing of magnetic fields at the center of a test pipe and validation of data by computer finite element analysis is described with the purpose of finding common results. The performance of the magnet configuration is evaluated with relation to the magnetic …


Computational Modeling Of Airborne Noise Demonstrated Via Benchmarks, Supersonic Jet, And Railway Barrier, Moumen Idres Jan 1999

Computational Modeling Of Airborne Noise Demonstrated Via Benchmarks, Supersonic Jet, And Railway Barrier, Moumen Idres

Mechanical & Aerospace Engineering Theses & Dissertations

In the last several years, there has been a growing demand for mobility to cope with the increasing population. All kinds of transportation have responded to this demand by expanding their networks and introducing new ideas. Rail transportation introduced the idea of high-speed trains and air transportation introduced the idea of high-speed civil transport (HSCT). In this expanding world, the noise legislation is felt to inhibit these plans. Accurate computational methods for noise prediction are in great demand.

In the current research, two computational methods are developed to predict noise propagation in air. The first method is based on the …


Setpoint Tracking Predictive Control In Chemical Processes Based On System Identification, Sinchai Chinvorarat Jan 1999

Setpoint Tracking Predictive Control In Chemical Processes Based On System Identification, Sinchai Chinvorarat

Mechanical & Aerospace Engineering Theses & Dissertations

A Kraft recovery boiler in a pulp-paper mill provides a means for recovery of the heat energy in spent liquor and recovery of inorganic chemicals while controlling emissions. These processes are carried out in a combined chemical recovery unit and steam boiler that is fired with concentrated black liquor and which produces molten smelt. Since the recovery boiler is considered to be an essential part of the pulp-paper mill in terms of energy resources, the performance of the recovery boiler has to be controlled to achieve the highest efficiency under unexpected disturbances.

This dissertation presents a new approach for combining …


Efficient Dynamic Unstructured Methods And Applications For Transonic Flows And Hypersonic Stage Separation, Xiaobing Luo Jan 1999

Efficient Dynamic Unstructured Methods And Applications For Transonic Flows And Hypersonic Stage Separation, Xiaobing Luo

Mechanical & Aerospace Engineering Theses & Dissertations

Relative-moving boundary problems have a wide variety of applications. They appear in staging during a launch process, store separation from a military aircraft, rotor-stator interaction in turbomachinery, and dynamic aeroelasticity.

The dynamic unstructured technology (DUT) is potentially a strong approach to simulate unsteady flows around relative-moving bodies, by solving time-dependent governing equations. The dual-time stepping scheme is implemented to improve its efficiency while not compromising the accuracy of solutions. The validation of the implicit scheme is performed on a pitching NACA0012 airfoil and a rectangular wing with low reduced frequencies in transonic flows. All the matured accelerating techniques, including the …


Continuous Adjoint Sensitivity Analysis For Aerodynamic And Acoustic Optimization, Kaveh Ghayour Jan 1999

Continuous Adjoint Sensitivity Analysis For Aerodynamic And Acoustic Optimization, Kaveh Ghayour

Mechanical & Aerospace Engineering Theses & Dissertations

A gradient-based shape optimization methodology based on continuous adjoint sensitivities has been developed for two-dimensional steady Euler equations on unstructured meshes and the unsteady transonic small disturbance equation. The continuous adjoint sensitivities of the Helmholtz equation for acoustic applications have also been derived and discussed.

The highlights of the developments for the steady two-dimensional Euler equations are the generalization of the airfoil surface boundary condition of the adjoint system to allow a proper closure of the Lagrangian functional associated with a general cost functional and the results for an inverse problem with density as the prescribed target. Furthermore, it has …


Design Optimization Of Magnetic Bearings And Magnetic Suspension Systems, V. Dale Bloodgood Jr. Oct 1998

Design Optimization Of Magnetic Bearings And Magnetic Suspension Systems, V. Dale Bloodgood Jr.

Mechanical & Aerospace Engineering Theses & Dissertations

Magnetic suspension systems were first demonstrated as practical by Holmes and Beams in the 1930's. Since then, numerous academic researchers have worked with various types of these systems. Commercial applications have largely been limited to magnetic bearings for rotating machinery. Other applications that have held considerable promise include wind tunnel model suspensions, space payload pointing and vibration isolation systems, satellite momentum storage and control devices and electromagnetic launch systems. However, none of these have progressed significantly beyond the prototype stage. Maglev trains have not reached serious commercial service but are being aggressively developed in Germany and Japan.

Design methods for …


Skin-Stiffener Separation In Buckled Composite Plates And Shallow Shells, Mark Edward Robeson Oct 1998

Skin-Stiffener Separation In Buckled Composite Plates And Shallow Shells, Mark Edward Robeson

Mechanical & Aerospace Engineering Theses & Dissertations

The development of an approximate analysis for predicting stresses in the skin-stiffener interface region of composite plates and shallow shells is presented. The analysis determines interlaminar normal stress and transverse shear stresses in the direction of the stiffener axial coordinate and the direction of the inplane coordinate perpendicular to the stiffener axis. The analysis accounts for skin-stiffener interfaces with nonzero thickness and for curvature in the skin and stiffener. The interlaminar normal stress and transverse shear stresses at the interface are applied to the lower face of the skin and the upper face of the stiffener flange as unknown functions, …


Saturation Control For Reduction Of Rotor Blade Lag Vibration, Sayam Saguanrum Oct 1998

Saturation Control For Reduction Of Rotor Blade Lag Vibration, Sayam Saguanrum

Mechanical & Aerospace Engineering Theses & Dissertations

Within the context of this research, the performance of saturation control for reduction in the vibratory lag motion of helicopter rotor blades is investigated. The single-degree-of-freedom plant, which consists of a spring and damper attached to the rotor blade, is perturbed by an aerodynamic force, and produces the unwanted vibration. To restrict this vibration, the second-order controller is provided to couple with the blade system. It works adaptively, when the system is excited and the controller frequency is set at half of the blade lag frequency in accordance with the relationship of both natural frequencies. The nonlinear terms from the …


Nonlinear Stability And Control Of Three-Dimensional Boundary Layers, Erik Janke Jul 1998

Nonlinear Stability And Control Of Three-Dimensional Boundary Layers, Erik Janke

Mechanical & Aerospace Engineering Theses & Dissertations

The linear and nonlinear evolution of steady and traveling disturbances in three-dimensional incompressible boundary layer flows is studied using Parabolized Stability Equations (PSE). Extensive primary stability analyses for the model problems of Swept Hiemenz flow and the DLR Transition experiment on a swept flat plate are performed first. Second, and building upon these results, detailed secondary instability studies based on both the classical Floquet Theory and a novel approach that uses the nonlinear PSE are conducted. The investigations reveal a connection of unstable secondary eigenvalues to both the linear eigenvalue spectrum of the undisturbed mean flow and the continuous spectrum, …


Approximate Analytical Relationships For Linear Optimal Aeroelastic Flight Control Laws, Ayman Hamdy Kassem Jul 1998

Approximate Analytical Relationships For Linear Optimal Aeroelastic Flight Control Laws, Ayman Hamdy Kassem

Mechanical & Aerospace Engineering Theses & Dissertations

This dissertation introduces new methods to uncover functional relationships between design parameters of a contemporary control design technique and the resulting closed-loop properties. Three new methods are developed for generating such relationships through analytical expressions: the Direct Eigen-Based Technique, the Order of Magnitude Technique, and the Cost Function Imbedding Technique. Efforts concentrated on the linear-quadratic state-feedback control-design technique applied to an aeroelastic flight control task. For this specific application, simple and accurate analytical expressions for the closed-loop eigenvalues and zeros in terms of basic parameters such as stability and control derivatives, structural vibration damping and natural frequency, and cost function …


Vortex Wake And Exhaust Plume Interaction, Including Ground Effect, Ihab Gaber Adam Jul 1998

Vortex Wake And Exhaust Plume Interaction, Including Ground Effect, Ihab Gaber Adam

Mechanical & Aerospace Engineering Theses & Dissertations

Computational modeling and studies of the near-field wake-vortex turbulent flows, far-field turbulent wake-vortex/exhaust-plume interaction for subsonic and High Speed Civil Transport (HSCT) airplane, and wake-vortex/exhaust-plume interaction with the ground are carried out. The three-dimensional, compressible Reynolds-Averaged Navier-Stokes (RANS) equations are solved using the implicit, upwind, Roe-flux-differencing, finite-volume scheme. The turbulence models of Baldwin and Lomax, one-equation model of Spalart and Allmaras and two-equation shear stress transport model of Menter are implemented with the RANS solver for turbulent-flow modeling.

For the near-field study, computations are carried out on a fine grid for a rectangular wing with a NACA-0012 airfoil section and …


Analysis And Testing Of Plates With Piezoelectric Sensors And Actuators, Jeffrey S. Bevan Apr 1998

Analysis And Testing Of Plates With Piezoelectric Sensors And Actuators, Jeffrey S. Bevan

Mechanical & Aerospace Engineering Faculty Publications

Piezoelectric material inherently possesses coupling between electrostatics and structural dynamics. Utilizing linear piezoelectric theory results in an intrinsically coupled pair of piezoelectric constitutive equations. One equation describes the direct piezoelectric effect where strains produce an electric field and the other describes the converse effect where an applied electrical field produces strain. The purpose of this study is to compare finite element analysis and experiments of a thin plate with bonded piezoelectric material. Since an isotropic plate in combination with a thin piezoelectric layer constitutes a special case of a laminated composite, the classical laminated plate theory is used in the …


Experimental Geometry Optimization Techniques For Multi-Element Airfoils, Drew Landman Apr 1998

Experimental Geometry Optimization Techniques For Multi-Element Airfoils, Drew Landman

Mechanical & Aerospace Engineering Theses & Dissertations

A study is reported on geometry optimization techniques for high-lift airfoils. A modern three-element airfoil model with a remotely actuated flap was designed, tested, and used in wind tunnel experiments to investigate optimum flap positioning based on lift. All the results presented were obtained in the Old Dominion University low-speed wind tunnel. Detailed results for lift coefficient versus flap vertical and horizontal position are presented for two airfoil angles-of-attack: 8 and 14 degrees. Three automated optimization simulations, the method of steepest ascent and two variants of the sequential simplex method, were demonstrated using experimental data. An on-line optimizer was demonstrated …


Reduction Of Thermal Deflection And Random Response Of Composite Structures With Embedded Shape Memory Alloy At Elevated Temperature, Zhiwei Zhong Apr 1998

Reduction Of Thermal Deflection And Random Response Of Composite Structures With Embedded Shape Memory Alloy At Elevated Temperature, Zhiwei Zhong

Mechanical & Aerospace Engineering Theses & Dissertations

A feasibility study on the reduction of thermal deflection and random response of the composite structures using shape memory alloys (SMA) at elevated temperatures is presented in this dissertation. The characteristics of SMA are introduced and the structural problems, static and dynamic, of SMA fiber reinforced composites are investigated. The stress-strain relations are developed for a composite lamina with embedded SMA fibers. The finite element system equations including shape memory effect are derived. A consistent two-step solution procedure is developed for solving the static and dynamic problems of composite structures with embedded SMA fibers subjected to combined acoustic and thermal …


The Design And Testing Of An Inlet-Airfoil For A High Altitude Remotely Piloted Aircraft, Preston Bradley Martin Apr 1998

The Design And Testing Of An Inlet-Airfoil For A High Altitude Remotely Piloted Aircraft, Preston Bradley Martin

Mechanical & Aerospace Engineering Theses & Dissertations

The following work describes and validates a methodology for the aerodynamic design of a low drag, efficient inlet-airfoil to be used on the cooling installations of a high altitude remotely piloted aircraft. Owing to the primary aircraft design requirement of subsonic endurance at high altitude (85,000 ft), the flight conditions present an aerodynamically unfavorable combination of low chord Reynolds number (500,000) and high subsonic Mach number (0.5). At this flight condition, the inlet-airfoil must meet the heat exchanger cooling flow requirements while maintaining the aerodynamic performance of the airfoil. As a result, the design method is closely coupled with not …


Placement Of Piezoelectric Actuators For Active Control Of Vibration Using Modal Parameters, Xuegeng Zhu Jan 1998

Placement Of Piezoelectric Actuators For Active Control Of Vibration Using Modal Parameters, Xuegeng Zhu

Mechanical & Aerospace Engineering Theses & Dissertations

An equation is derived to model the piezoelectric actuators incorporation with flexible structures. This equation permits the comparison of the performance indices over the entire structure for a piezoelectric actuator with constant area, which is unachievable if the Finite Element Method is used for complicated structures.

An index has been developed for placement of piezoelectric actuator for control of vibration of a flexible structure. This index is derived from the definition of H2norm. Computation of the proposed index requires only the natural frequencies and corresponding mode shapes of the structures of interest. The method is well suited to large …


Thermal And Mechanical Behavior Of Cryogenic Propellant Tank Concepts For Advanced Launch Vehicles, H. Kevin Rivers Oct 1997

Thermal And Mechanical Behavior Of Cryogenic Propellant Tank Concepts For Advanced Launch Vehicles, H. Kevin Rivers

Mechanical & Aerospace Engineering Theses & Dissertations

An important step in developing a cost-effective, fully-reusable, launch vehicle is the development of durable, lightweight, insulated, cryogenic propellant tanks. Current cryogenic tanks are expendable, and much of the technology that exist is not usable on future vehicles. As part of the Reusable Launch Vehicle/ X-33 Program, an experimental apparatus for evaluating the effects of both thermal and mechanical loading on cryogenic-tank concepts was developed at the NASA Langley Research Center. Studies to determine the behavior of various liquid-oxygen- and liquid-hydrogen-tank concepts under simulated mission conditions were performed as part of this research and are reported. Selected analytical studies of …


Interactive Approach For Geometry Definition With Automatically Differentiated Sensitivities For Practical Airplane Design, Yvette Cordero Jul 1997

Interactive Approach For Geometry Definition With Automatically Differentiated Sensitivities For Practical Airplane Design, Yvette Cordero

Mechanical & Aerospace Engineering Theses & Dissertations

First, a newly developed interactive surface generation tool is described for the conceptual design phase and aerodynamic shape optimization of aircraft. The new design tool is called Interactive Rapid Airplane Parametric Input Design (IRAPID) for fuselage and wing body configurations, and Blended Wing Body (BWB) generator for flying wing configurations. The development of the software is based on the RAPID methodology, which incorporates a partial differential equation approach to surface design. By incorporating physical airplane design parameters into the boundaty conditions of the partial differential equation, the solution surface of a wing configuration is generated. The construction of fuselage components …


Reverse Engineering Of Aircraft Wing Data Using A Partial Differential Equation Surface Model, Jacalyn M. Huband Jul 1997

Reverse Engineering Of Aircraft Wing Data Using A Partial Differential Equation Surface Model, Jacalyn M. Huband

Mathematics & Statistics Theses & Dissertations

Reverse engineering is a multi-step process used in industry to determine a production representation of an existing physical object. This representation is in the form of mathematical equations that are compatible with computer-aided design and computer-aided manufacturing (CAD/CAM) equipment. The four basic steps to the reverse engineering process are data acquisition, data separation, surface or curve fitting, and CAD/CAM production. The surface fitting step determines the design representation of the object, and thus is critical to the success or failure of the reverse engineering process. Although surface fitting methods described in the literature are used to model a variety of …


A Comparison Between Simulated And Measured Free-Flight Vortex Encounter Behavior In The Nasa Langley Full-Scale Wind Tunnel, Robert A. Pfouts Jul 1997

A Comparison Between Simulated And Measured Free-Flight Vortex Encounter Behavior In The Nasa Langley Full-Scale Wind Tunnel, Robert A. Pfouts

Mechanical & Aerospace Engineering Theses & Dissertations

An examination of the use of static measurements in simulating dynamic aircraft­ wake encounters is presented. By comparing dynamic aircraft-wake vortex encounter measurements obtained in free-flight wind tunnel tests to data obtained from computer­ simulated encounters based on static wind tunnel data, a determination is made concerning the validity of static vortex models in a dynamic flight environment. The development and testing of specialized elements of a flight simulation code are presented and dynamic free-flight measurements and predicted results are compared.

This study shows that static modeling provides reasonable estimates for lateral encounter trajectories when the following aircraft model is …


Three-Dimensional Aerodynamic Design Optimization Using Discrete Sensitivity Analysis And Parallel Computing, Amidu Olawale Oloso Apr 1997

Three-Dimensional Aerodynamic Design Optimization Using Discrete Sensitivity Analysis And Parallel Computing, Amidu Olawale Oloso

Mechanical & Aerospace Engineering Theses & Dissertations

A hybrid automatic differentiation/incremental iterative method was implemented in the general purpose advanced computational fluid dynamics code (CFL3D Version 4.1) to yield a new code (CFL3D.ADII) that is capable of computing consistently discrete first order sensitivity derivatives for complex geometries. With the exception of unsteady problems, the new code retains all the useful features and capabilities of the original CFL3D flow analysis code. The superiority of the new code over a carefully applied method of finite-differences is demonstrated.

A coarse grain, scalable, distributed-memory, parallel version of CFL3D.ADII was developed based on "derivative stripmining". In this data-parallel approach, an identical copy …


Broadband Dynamic Modification Using Feedforward Control, Kendeas Antonis Karantonis Apr 1997

Broadband Dynamic Modification Using Feedforward Control, Kendeas Antonis Karantonis

Mechanical & Aerospace Engineering Theses & Dissertations

The use of feedforward control for dynamic modification is relatively new to the area of structural vibration control. In this thesis the disturbance path dynamics of a flexible aluminum beam, pinned at both ends and under the influence of broadband excitation inputs, are modified through the use of feedforward control. The ideal algebraically determined feedforward control method for response cancellation is first presented. Theoretically, this compensator modifies the disturbance path dynamics to any desired behavior. This ideal algebraic approach can only be used for minimum phase systems. In non-minimum phase systems, right half s-plane plant zeros emerge as unstable poles …


Investigation Of An Alternative Technique For Measuring Turbulence In The Upper Atmosphere, Charles Patrick Leonard Apr 1997

Investigation Of An Alternative Technique For Measuring Turbulence In The Upper Atmosphere, Charles Patrick Leonard

Mechanical & Aerospace Engineering Theses & Dissertations

The capability of the Global Positioning System (GPS) as a tool for measuring turbulence in the upper atmosphere is presented. By studying experimental ground and flight test data, a methodology for extracting macroscale turbulence data from in situ measurements was developed.

A description of the GPS using a single nonprecision receiver is followed by data from ground and flight testing. Ground testing focused on determining the smallest turbulent scales discernible by the GPS receiver. Testing was also undertaken to compare turbulence data from the GPS with that of a simultaneously operating constant-temperature hot-wire anemometer, the conventional tool for making turbulence …


Aerodynamic Gradient-Based Optimization Using Computational Fluid Dynamics And Discrete Sensitivities For Practical Problems, Mohagna Jayendrarai Pandya Apr 1997

Aerodynamic Gradient-Based Optimization Using Computational Fluid Dynamics And Discrete Sensitivities For Practical Problems, Mohagna Jayendrarai Pandya

Mechanical & Aerospace Engineering Theses & Dissertations

A gradient-based shape optimization methodology based on quasi-analytical sensitivities has been developed for practical three-dimensional aerodynamic applications. The flow analysis has been rendered by a fully implicit, finite-volume formulation of the Euler and Thin Layer Navier-Stokes (TLNS) equations. The flow equations and aerodynamic sensitivity equation have been solved using an alternating-direction-implicit (ADI) algorithm for memory efficiency. A wing geometry model based on space-surface and planform parameterization has been utilized. The present methodology and its components have been tested via several comparisons.

Initially, the inviscid flow analysis for a wing has been compared with those obtained using an unfactored, Preconditioned Conjugate …


Input Design For Systems Under Identification Using Indirect And Direct Methods, Marco P. Schoen Mar 1997

Input Design For Systems Under Identification Using Indirect And Direct Methods, Marco P. Schoen

Mechanical & Aerospace Engineering Theses & Dissertations

The motivation for system identification can be manifold. In this work, the provocation to identify unknown system characteristics is derived from the control engineering point of view. That is, one intends to design a control strategy based on the identified system properties. The used system identification methods are the Open-Loop Kalman filter System Identification method (OKID) and the Closed-Loop System Identification method (CLID). It is shown that the quantitative largest error of the system identification is given by its model representation, that is the attempt to describe a system with model parameters which poses a linear relationship with the input/output …


Parametric Correlations For Generic Scramjet Combustors With Ramp-Type Injectors, Jason Granville Bush Oct 1996

Parametric Correlations For Generic Scramjet Combustors With Ramp-Type Injectors, Jason Granville Bush

Mechanical & Aerospace Engineering Theses & Dissertations

Development of an efficient scramjet combustor requires the use of computational models due to the cost of full-scale physical testing in the speed regime of Mach 10 through Mach 18. This study focuses upon the database generated by one such computational model, SHIP3D, which describes a generic scramjet combustor using ramp-type file! injectors. Three generalized parametric equations have been developed from this database, which describe the fuel-air mixing efficiency within the scramjet combustor as a function of normalized-axial combustor distance, ramp injector-region lift coefficient, and stoichiometry. It is shown that one of the three equations nearly models the trends as …


Dynamics And Control Of A Three Dimensional Gantry Crane With Cable Flexibility, Uchendu H. Eke Oct 1996

Dynamics And Control Of A Three Dimensional Gantry Crane With Cable Flexibility, Uchendu H. Eke

Mechanical & Aerospace Engineering Theses & Dissertations

The control of payload swing in industrial gantry cranes is a topic of widespread interest. In this thesis, the control of the swing of a payload idealized by a point mass assumption is investigated utilizing s, compact robotics matrix/vector representation of the dynamical model. In this form, this particular system can be viewed as sn underactuated manipulator with equal numbers of active and passive degrees of freedom. The full three dimensional model is developed and linearized by modelling the cable as a single thread of fiexible wire and the degree of dynamic coupling between the active and passive coordinates is …