A Geometric Unification of Constrained System Dynamics

A unified geometric formulation of the methods used for solving constrained system problems is given. Both holonomic and nonholonomic systems are treated in like manner, and the dynamic equations are expressible in either generalized velocities or quasi-velocities. Moreover, a wide range of ’unconstrained‘ systems are uniformly regarded as generalized particles in the multi-dimensional metric spaces relating to their configuration. The derivation is grounded on the tensor calculus formalism and appropriate geometric interpretations are reported. In its useful matrix form, the formulation turns out short, elementary and general. This unified geometric approach to constrained system dynamics may deserve to become a generally accepted method inacademic and engineering applications.

[1]  W. C. Walton,et al.  A new matrix theorem and its application for establishing independent coordinates for complex dynamical systems with constraints , 1969 .

[2]  I. Neĭmark,et al.  Dynamics of Nonholonomic Systems , 1972 .

[3]  J. Baumgarte.  Stabilization of constraints and integrals of motion in dynamical systems , 1972 .

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

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

[6]  M. A. Chace,et al.  A Sparsity-Oriented Approach to the Dynamic Analysis and Design of Mechanical Systems—Part 1 , 1977 .

[7]  N. Orlandea,et al.  A Sparsity-Oriented Approach to the Dynamic Analysis and Design of Mechanical Systems—Part 2 , 1977 .

[8]  Thomas R. Kane,et al.  Formulation of Equations of Motion for Complex Spacecraft , 1980 .

[9]  Hooshang Hemami,et al.  Modeling of Nonholonomic Dynamic Systems With Applications , 1981 .

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

[11]  N. K. Mani,et al.  Application of Singular Value Decomposition for Analysis of Mechanical System Dynamics , 1985 .

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

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

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

[15]  J. García de Jalón,et al.  Natural coordinates for the computer analysis of multibody systems , 1986 .

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

[17]  J. G. Jalón,et al.  Dynamic Analysis of Three-Dimensional Mechanisms in “Natural” Coordinates , 1987 .

[18]  George M. Lance,et al.  A Differentiable Null Space Method for Constrained Dynamic Analysis , 1987 .

[19]  S. K. Ider,et al.  A recursive householder transformation for complex dynamical systems with constraints , 1988 .

[20]  E. A. Desloge,et al.  The Gibbs–Appell equations of motion , 1988 .

[21]  Dan Scott,et al.  Can a projection method of obtaining equations of motion compete with Lagrange’s equations? , 1988 .

[22]  Parviz E. Nikravesh,et al.  Computer-aided analysis of mechanical systems , 1988 .

[23]  P. Maisser.  Analytische Dynamik von Mehrkörpersystemen , 1988 .

[24]  F. Cardin,et al.  On constrained mechanical systems: D’Alembert’s and Gauss’ principles , 1989 .

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

[26]  Linda R. Petzold,et al.  Methods and Software for Differential-Algebraic Systems , 1990 .

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

[28]  M. Lesser.  A geometrical interpretation of Kane’s Equations , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[29]  Wojciech Blajer.  A Projection Method Approach to Constrained Dynamic Analysis , 1992 .

[30]  W. Blajer.  Projective formulation of Maggi's method for nonholonomic systems analysis , 1992 .

[31]  W. Schiehlen,et al.  A projective criterion to the coordinate partitioning method for multibody dynamics , 1994, Archive of Applied Mechanics.

[32]  H. Essén.  On the Geometry of Nonholonomic Dynamics , 1994 .

[33]  Wojciech Blajer,et al.  An orthonormal tangent space method for constrained multibody systems , 1995 .

[34]  W. Blajer,et al.  A unified approach to the modelling of holonomic and nonholonomic mechanical systems , 1996 .