Novel Dynamics and Controls Analysis Methods for Nonlinear Structural Systems

Abstract : Significant progress is reported on analytical and computational methodology applicable to dynamics and control of flexible multibody structures. Especially significant are the following: (1) We have developed new analytical and numerical results pertaining to imposing constraints in multi-body dynamical modeling and numerical simulation. We have developed an extension of existing penalty methods for constrained multibody dynamics, including some significant convergence proofs. (2) We have developed a power principle which permits the efficient construction of stabilizing control laws for systems described by nonlinear systems of coupled ordinary and partial differential equations. (3) We have initiated a study of symbol manipulation methods to derive polynomial-type nonlinear feedback control laws for dynamical systems with polynomial nonlinearities. A general MACSYMA symbolic computer code has been developed and studies are under way on several test problems. (kr)

[1]  J. Z. Zhu,et al.  The finite element method , 1977 .

[2]  Toshiyuki Ohtsuka,et al.  Mission function control for a slew maneuver experiment , 1991 .

[3]  Dewey H. Hodges,et al.  Weak Hamiltonian finite element method for optimal control problems , 1991 .

[4]  R. Alexander,et al.  Runge-Kutta methods and differential-algebraic systems , 1990 .

[5]  Linda R. Petzold,et al.  On order reduction for Runge-Kutta methods applies to differential algebraic systems and to stiff systems of ODEs , 1990 .

[6]  S. N. Rasband,et al.  Chaotic Dynamics of Nonlinear Systems , 1990 .

[7]  John L. Junkins,et al.  Near-minimum-time maneuvers of flexible vehicles - A Liapunov control law design method , 1990 .

[8]  Suresh M. Joshi,et al.  Control of Large Flexible Space Structures , 1989 .

[9]  Eduardo Bayo,et al.  Penalty Formulations for the Dynamic Analysis of Elastic Mechanisms , 1989 .

[10]  M. A. Serna,et al.  A modified Lagrangian formulation for the dynamic analysis of constrained mechanical systems , 1988 .

[11]  Andrew J. Kurdila,et al.  Concurrent multiprocessing methods for calculating nullspace and range space bases for multibody simulation , 1988 .

[12]  E. Zeidler.  Nonlinear functional analysis and its applications , 1988 .

[13]  Edward J. Haug,et al.  A Hybrid Numerical Integration Method for Machine Dynamic Simulation , 1986 .

[14]  S. S. Kim,et al.  QR Decomposition for State Space Representation of Constrained Mechanical Dynamic Systems , 1986 .

[15]  P. Likins,et al.  Singular Value Decomposition for Constrained Dynamical Systems , 1985 .

[16]  J. Tinsley Oden,et al.  Qualitative methods in nonlinear mechanics , 1985 .

[17]  C. Wampler,et al.  Formulation of Equations of Motion for Systems Subject to Constraints , 1985 .

[18]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[19]  Philip E. Gill,et al.  Practical optimization , 1981 .

[20]  Roy R. Craig,et al.  Structural Dynamics: An Introduction to Computer Methods , 1981 .

[21]  John M. Hollerbach,et al.  A Recursive Lagrangian Formulation of Maniputator Dynamics and a Comparative Study of Dynamics Formulation Complexity , 1980, IEEE Transactions on Systems, Man, and Cybernetics.

[22]  C. W. Gear,et al.  Numerical initial value problem~ in ordinary differential eqttations , 1971 .

[23]  Leonard Meirovitch,et al.  Methods of analytical dynamics , 1970 .

[24]  J. Junkins,et al.  On the existence of limit cycles for a class of penalty formulations of dissipative multibody systems , 1990 .

[25]  A. Kurdila,et al.  Role of Maggi's Equations in Computational Methods for Constrained Multibody Systems , 1990 .

[26]  E. J. Dean,et al.  On the discretization of some second order in time differential equations - Applications to nonlinear wave problems , 1990 .

[27]  Sunil Saigal,et al.  Dynamic analysis of multi-body systems using tangent coordinates , 1989 .

[28]  J. W. Sunkel,et al.  Computationally efficient algorithm for the dynamics of multi-link mechanisms , 1989 .

[29]  R. L. Huston,et al.  Useful Procedures in Multibody Dynamics , 1986 .

[30]  J. Junkins,et al.  Optimal Spacecraft Rotational Maneuvers , 1986 .

[31]  Edward J. Haug,et al.  Elements and Methods of Computational Dynamics , 1984 .

[32]  J. Oden.  Finite Elements: A Second Course , 1983 .

[33]  C. K. CARRINGTON,et al.  Optimal nonlinear feedback control for spacecraft attitude maneuvers , 1983 .

[34]  E. Haug,et al.  Generalized Coordinate Partitioning for Dimension Reduction in Analysis of Constrained Dynamic Systems , 1982 .

[35]  J. A. Walker,et al.  Dynamical Systems and Evolution Equations , 1980 .

[36]  J. Wittenburg,et al.  Dynamics of systems of rigid bodies , 1977 .

[37]  Edward L. Wilson,et al.  Numerical methods in finite element analysis , 1976 .

[38]  V. Arnold.  Mathematical Methods of Classical Mechanics , 1974 .

[39]  C. W. Gear,et al.  Simultaneous Numerical Solution of Differential-Algebraic Equations , 1971 .