Stereodynamics: Lectures given at a Summer School of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Bressanone (Bolzano), Italy, June 2-12, 1971 (C.I.M.E. Summer Schools, 56)

G. Grioli: Particular solutions in stereodynamics.- P. Hagedorn: On the converse of the Lagrange-Dirichlet stability theorem.- M. Langlois: Contribution à l’étude du mouvement du corps rigide à n dimensions autour d’un point fixe.- E. Leimanis: Some recent results concerning the motion of a rigid body about a fixed point.- H. Price: A canonical form of Euler’s equations and a method of solutions for arbitrary applied couples.- V.V. Rumyentsev: Dynamics and stability of rigid bodies.- J. Wittenburg: The dynamics of systems of coupled rigid bodies. A new general formalism with applications. Cover Stereodynamics ISBN 9783642109904 Contents Cenni Introduttivi I Solido Pesante II IL Giroscopio a Reazione III Sulla Dinamica di un Corpo Rigido in un Campo Newtoniano Centrale IV Sul Principio Dell'effetto Giroscopico V Precessioni Generalizzate Bibliografia On The Converse of Lagrange - Dirichlet's Stability Theorem References Contribution a L'etude du Mouvement du Corps Rigide an Dimensions Autour D'un Point Fixe Bibliographie I. Quelques Aspects Cinematiques de La Rotation du Corps Solide an Dimensions Autour D'un Point Fixe II. Generalisation des Theoremes D'Euler du Mouvement D'euler - Poinsot au Mouvement du Corps Rigide an Dimensions Autour D'un Point Fixe III. Application - Quelques Proprietes des Equations D'euler Dans R4 Some recent results conceraing the motion of a rigid body about a fixed point I Reduction of the order of the Euler and Poisson equations 1. Equations of motion of a heavy rigid body 2. Equations of motion of a gyrostant 3. The number of arbitrary constants 5. Reduction of the equations of motion to a single equation II Kinematic interpretation of the motion 1. The moving and fixed hodographs 2. The Hess solution III. Existence of invariant relations of equations of motion 1. Linear invariant relation 2. The kinematic interpretation of the motion in the case 3. Quadratic invariant relation Bibliography A Canonical from of Euler's Equationd and a Method of Solution for Arbitrary Applied Couples Summary Reduction of the Equations to Canonical form The Zero-Order Solution The First-Order Solution The Second -Order Solution Brief Report on a Numerical Example Runge - Kutta Method Mothod of this paper Dynamics and Stability of Rigid Bodies References The Dynamics of Systems of Coupled rigid Bodies a new General Formalism with Applications 1. Introduction 2. Description of the System 3. Notation 4. The Equations of motion 5. The Kinetic Energy 6. The Dynamical Equations of Motion of an n-body System with one Point Fixed in Inertial Space 7. A Special Case Plane Motions of Chains 8. First Application: The Multi-Body Satellite in a Circular Orbit The Dynamic Potential Energy 9. Second Application : Impact Problems in Multi-Body Systems The Law of Maxwell and Betti in Dynamics Dynamical Equations for Impacts on Elementary Systems Kinematical Equations for Elementary Systems An Illustrative Example : The Collision of a Chain with Itself Literature references Langlois: Contribution a l'etude du mouvement du corps rigide a n dimensions autour d'un point fixe.- E. Leimanis: Some recent results concerning the motion of a rigid body about a fixed point.- H. Rumyentsev: Dynamics and stability of rigid bodies.- J. Wittenburg: The dynamics of systems of coupled rigid bodies.