Dynamics of systems of rigid bodies

Inhaltsverzeichnis1 Mathematical Notation.2 Rigid Body Kinematics.2.1 Generalized coordinates for the angular orientation of a rigid body.2.1.1 Euler angles.2.1.2 Bryant angles.2.1.3 Euler parameters.2.2 The notion of angular velocity.2.3 Relationships between the angular velocity of a body and generalized coordinates describing the angular orientation of the body.2.3.1 Direction cosines.2.3.2 Euler angles.2.3.3 Bryant angles.2.3.4 Euler parameters.3 Basic Principles of Rigid Body Dynamics.3.1 Kinetic energy.3.2 Angular momentum.3.3 Properties of moments and products of inertia.3.3.1 Transition to another reference point without change of the reference base.3.3.2 Transition to another reference base without change of the reference point.3.3.3 Principal axes and principal moments of inertia.3.3.4 Invariants and inequalities for moments and products of inertia.3.4 The law of moment of momentum.3.5 D’Alembert’s principle applied to a rigid body.4 Classical Problems of Rigid Body Mechanics.4.1 The unsymmetric torque-free rigid body.4.1.1 Polhodes and permanent rotations.4.1.2 Poinsot’s geometric interpretation of the motion.4.1.3 The solution of Euler’s equations of motion.4.1.4 The solution of the kinematic differential equations.4.2 The symmetric torque-free rigid body.4.3 The self-excited, symmetric rigid body.4.4 The symmetric heavy top.4.5 The symmetric heavy body in a cardan suspension.4.6 The gyrostat. General considerations.4.7 The torque-free gyrostat.4.7.1 Polhodes and permanent rotations.4.7.2 The solution of the dynamic equations of motion.5 General Multi-Body Systems.5.1 Introductory remarks.5.2 Equations of motion for systems with tree structure.5.2.1 The mathematical description of the interconnection structure.5.2.2 Systems with ball-and-socket joints. One body is coupled to an external body whose motion is prescribed.5.2.3 The special case of plane motions.5.2.4 Systems with ball-and-socket joints without coupling to an external body whose motion is prescribed.5.2.5 The special case of a multi-body satellite in a circular orbit.5.2.6 Systems with ball-and-socket, universal and pin joints.5.2.7 Programming instructions.5.2.8 Systems with arbitrary holonomic constraints in the hinges.5.2.9 Internal forces and torques in the hinges of a system with arbitrary holonomic constraints.5.3 Multi-body systems with closed chains and with arbitrary constraints.5.3.1 The mathematical description of the interconnection structure. A generalization of Section 5.2.1.5.3.2 Equations of motion.5.4 Concluding remarks.6 Impact Problems in Holonomic Multi-Body Systems.6.1 Basic assumptions.6.2 Instantaneous velocity increments.6.3 An analogy to the law of Maxwell and Betti.6.4 Internal impulses and impulse couples in hinges.Answers to Problems.Literature References.