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comparison of a special purpose processor with a general purpose processor and a numerical approach in generating helicopter dynamics equations
Title
A comparison of a special purpose processor with a general purpose processor and a numerical approach in generating helicopter dynamics equations.
Creator
Ravichandran, S., Florida Atlantic University, Gaonkar, Gopal H., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description
Presently three schemes are used to generate the governing equations of motion. These schemes are: (1) general purpose processors such as REDUCE, MACSYMA and MAPLE, (2) a special purpose symbolic processor DEHIM--Dynamic Equations for Helicopter Interpretive Models and (3) completely numerical approaches such as AGEM--Automatic Generation of Equations of Motion. With REDUCE as a representative multipurpose processor in scheme 1, comparative aspects of these three schemes have been studied by...
Show morePresently three schemes are used to generate the governing equations of motion. These schemes are: (1) general purpose processors such as REDUCE, MACSYMA and MAPLE, (2) a special purpose symbolic processor DEHIM--Dynamic Equations for Helicopter Interpretive Models and (3) completely numerical approaches such as AGEM--Automatic Generation of Equations of Motion. With REDUCE as a representative multipurpose processor in scheme 1, comparative aspects of these three schemes have been studied by applying them to the same set of problems. These problems range from a linear model of a single blade with one degree of freedom to a mildly nonlinear three-bladed rotor model with several degrees of freedom. The derivation process includes the nonlinear equations and the perturbed linear equations about a user-supplied equilibrium state in a rotating frame and then the multiblade equations, which represent transformation into a nonrotating frame using multiblade coordinates. (Abstract shortened with permission of author.)
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Date Issued
1989
PURL
http://purl.flvc.org/fcla/dt/14517
Subject Headings
Algebra--Computer programs, Helicopters--Dynamics
Format
Document (PDF)
Trim analysis by shooting and finite elements and Floquet eigenanalysis by QR and subspace iterations in helicopter dynamics
Title
Trim analysis by shooting and finite elements and Floquet eigenanalysis by QR and subspace iterations in helicopter dynamics.
Creator
Achar, Nagari Shriranga., Florida Atlantic University, Gaonkar, Gopal H., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description
The trim analysis for the initial state and control inputs that satisfy response periodicity and flight conditions, and the Floquet eigenanalysis for a few largest eigenvalues of the Floquet transition matrix (FTM) are investigated. In the trim analysis, the convergence of Newton iteration is investigated in computing the periodic initial state and control inputs sequentially and in parallel. The trim analysis uses the shooting method and two h-versions of temporal finite element methods, one...
Show moreThe trim analysis for the initial state and control inputs that satisfy response periodicity and flight conditions, and the Floquet eigenanalysis for a few largest eigenvalues of the Floquet transition matrix (FTM) are investigated. In the trim analysis, the convergence of Newton iteration is investigated in computing the periodic initial state and control inputs sequentially and in parallel. The trim analysis uses the shooting method and two h-versions of temporal finite element methods, one based on displacement formulation and the other on mixed formulation of displacements and momenta. In each method, both the sequential and in-parallel schemes are used, and the resulting nonlinear equations are solved by damped Newton iteration with an optimally selected damping parameter. The reliability of damped Newton iteration, including earlier-observed divergence problems, is quantified by the maximum condition number of the Jacobian matrices of the iterative scheme. For illustrative purposes, rigid flap-lag and flap-lag-torsion models based on quasisteady aerodynamics are selected. Demanding trim analysis conditions are included by considering advance ratios or dimensionless flight speeds twice as high as those of current helicopters. Concerning the Floquet eigenanalysis, the feasibility of using the Arnoldi-Saad method, one of the emerging subspace iteration methods, is explored as an alternative to the currently used QR method, which is not economical for partial eigenanalysis. The reliability of the Arnoldi-Saad method is quantified by the eigenvalue condition numbers and the residual errors of the eigenpairs. In the three trim analysis methods, while the optimally selected damping parameter provides almost global convergence, the in-parallel scheme requires much less machine time than the conventional sequential scheme; both schemes have comparable reliability of the Newton iteration without and with damping. The Arnoldi-Saad method takes much less machine time than the QR method with comparable reliability.
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Date Issued
1992
PURL
http://purl.flvc.org/fcla/dt/12297
Subject Headings
Helicopters--Dynamics, Helicopters--Handling characteristics, Stability of helicopters--Mathematical models
Format
Document (PDF)