Hybrid equations of motion for flexible multibody systems using quasicoordinates

A variety of engineering systems, such as automobiles, aircraft, rotorcraft, robots, spacecraft, etc., can be modeled as flexible multibody systems. The individual flexible bodies are in general characterized by distributed parameters. In most earlier investigations they were approximated by some spatial discretization procedure, such as the classical Rayleigh-Ritz method or the finite element method. This paper presents a mathematical formulation for distributed-parameter multibody systems consisting of a set of hybrid (ordinary and partial) differential equations of motion in terms of quasi-coordinates. Moreover, the equations for the elastic motions include rotatory inertia and shear deformation effects. The hybrid set is cast in state form, thus making it suitable for control design.

[1]  Ahmed A. Shabana,et al.  A Recursive Formulation for the Dynamic Analysis of Open Loop Deformable Multibody Systems , 1988 .

[2]  Edward J. Haug,et al.  Dynamics of Articulated Structures. Part II. Computer Implementation and Applications , 1986 .

[3]  E. Haug.  Dynamics of articulated structures , 1989 .

[4]  E. Haug,et al.  Dynamics of Articulated Structures. Part I. Theory , 1986 .

[5]  Shir-Kuan Lin,et al.  A new composite body method for manipulator dynamics , 1991, J. Field Robotics.

[6]  W. Book.  Recursive Lagrangian Dynamics of Flexible Manipulator Arms , 1984 .

[7]  John L. Junkins,et al.  Explicit generalization of Lagrange's equations for hybrid coordinate dynamical systems , 1992 .

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

[9]  R. D. Quinn.  Equations of Motion for Structures in Terms of Quasi-Coordinates , 1990 .

[10]  R. Quinn,et al.  Equations of motion for maneuvering flexible spacecraft , 1987 .

[11]  L. Meirovitch,et al.  New approach to the maneuvering and control of flexible multibody systems , 1992 .

[12]  K. H. Lowl.  A systematic formulation of dynamic equations for robot manipulators with elastic links , 1987, J. Field Robotics.

[13]  R. Judd,et al.  Dynamics of nonrigid articulated robot linkages , 1985 .

[14]  J.Y.L. Ho,et al.  Direct Path Method for Flexible Multibody Spacecraft Dynamics (Originally schedulled for publication in the AIAA Journal) , 1977 .

[15]  S. S. Kim,et al.  A General and Efficient Method for Dynamic Analysis of Mechanical Systems Using Velocity Transformations , 1986 .

[16]  Thomas R. Kane,et al.  The Use of Kane's Dynamical Equations in Robotics , 1983 .

[17]  E. J. Haug,et al.  Computer aided kinematics and dynamics of mechanical systems. Vol. 1: basic methods , 1989 .

[18]  Ronald L. Huston,et al.  Dynamics of Multibody Systems , 1988 .

[19]  L. Meirovitch,et al.  Maneuvering and control of flexible space robots , 1994 .

[20]  J. C. Simo,et al.  Dynamics of earth-orbiting flexible satellites with multibody components , 1987 .

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

[23]  E. Haug.  Computer Aided Analysis and Optimization of Mechanical System Dynamics , 1984 .

[24]  Leonard Meirovitch,et al.  Hybrid state equations of motion for flexible bodies in terms of quasi-coordinates , 1991 .

[25]  H. D. Nelson,et al.  On the high-spin motion of a satellite containing elastic parts. , 1966 .

[26]  R. Huston,et al.  Dynamics of Multirigid-Body Systems , 1978 .

[27]  L. Meirovitch,et al.  Rayleigh-Ritz Based Substructure Synthesis for Flexible Multibody Systems , 1991 .

[28]  William M. Silver.  On the Equivalence of Lagrangian and Newton-Euler Dynamics for Manipulators , 1982 .

[29]  Leonard Meirovitch,et al.  Computational Methods in Structural Dynamics , 1980 .

[30]  Ronald L. Huston,et al.  Flexibility effects in multibody system dynamics , 1980 .