The theory of pseudo-rigid bodies.

*(English)*Zbl 0687.70001
Springer Tracts in Natural Philosophy, 33. New York etc.: Springer-Verlag. x, 183 p. DM 128.00 (1988).

The theory of elastic pseudo-rigid bodies focuses on the large-scale motions of elastic deformable bodies. Essential is the fact that this theory (based on special directed continua) comprises a dynamical system with finitely many degrees of freedom. The theory may therefore be viewed either as a generalization of the classical mechanics of a rigid body or as a restriction of the classical theory of elastic bodies.

Chapter 2 of this well written book deals with the foundations of the theory using an axiomatic treatment in which a pseudo-rigid body is modeled as a directed continuum.

A comparison of this theory with some three dimensional continuum theories is given in chapter 3. The authors develop the concept of a subtheory, which entails the specification of a mapping, through which direct comparisons between theories are possible.

Chapter 4 considers the solution of selected problems and the development of perturbation methods. The authors examine Lagrangian and Hamiltonian formulations in chapter 5, using the fact that the configuration manifold of their theory is a Lie group.

Chapter 6 deals with almost rigid bodies. The perturbation analysis of the motion of a pseudo-rigid body in the neighborhood of a rigid state involves a two-time scale asymptotic representation of solutions to highlight the interplay between the effects of deformation and rotation of the bodies.

This monograph is of interest for scientists in the fields of analytical mechanics, multi body dynamics and continuum theory.

Chapter 2 of this well written book deals with the foundations of the theory using an axiomatic treatment in which a pseudo-rigid body is modeled as a directed continuum.

A comparison of this theory with some three dimensional continuum theories is given in chapter 3. The authors develop the concept of a subtheory, which entails the specification of a mapping, through which direct comparisons between theories are possible.

Chapter 4 considers the solution of selected problems and the development of perturbation methods. The authors examine Lagrangian and Hamiltonian formulations in chapter 5, using the fact that the configuration manifold of their theory is a Lie group.

Chapter 6 deals with almost rigid bodies. The perturbation analysis of the motion of a pseudo-rigid body in the neighborhood of a rigid state involves a two-time scale asymptotic representation of solutions to highlight the interplay between the effects of deformation and rotation of the bodies.

This monograph is of interest for scientists in the fields of analytical mechanics, multi body dynamics and continuum theory.

Reviewer: G.P.Ostermeyer

##### MSC:

70-02 | Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems |

74-02 | Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids |

74A99 | Generalities, axiomatics, foundations of continuum mechanics of solids |

70E99 | Dynamics of a rigid body and of multibody systems |

74Axx | Generalities, axiomatics, foundations of continuum mechanics of solids |

70B99 | Kinematics |