Dynamics of Systems of Rigid Bodies: 33 - Brossura

Wittenburg, Jens

Brossura

ISBN 10: 3322909433 ISBN 13: 9783322909435

Casa editrice: Vieweg+Teubner Verlag, 2012

Riassunto

A system of rigid bodies in the sense of this book may be any finite number of rigid bodies interconnected in some arbitrary fashion by joints with ideal holonomic, nonholonomic, scleronomic and/or rheonomic constraints. Typical examples are the solar system, mechanisms in machines and living mechanisms such as the human body provided its individual members can be considered as rigid. Investigations into the dynamics of any such system require the formulation of nonlinear equations of motion, of energy expressions, kinematic relationships and other quantities. It is common practice to develop these for each system separately and to consider the labor necessary for deriving, for example, equations of motion from Lagrange's equation, as inevitable. It is the main purpose of this book to describe in detail a formalism which substantially simplifies these tasks. The formalism is general in that it provides mathematical expressions and equations which are valid for any system of rigid bodies. It is flexible in that it leaves the choice of generalized coordinates to the user. At the same time it is so explicit that its application to any particular system requires only little more than a specification of the system geometry. The book is addressed to advanced graduate students and to research workers. It tries to attract the interest of the theoretician as well as of the practitioner.

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Contenuti

1 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.

Dettagli dell'edizione

• Editore: Vieweg+Teubner Verlag
• Data di pubblicazione: 2012
• Lingua: Tedesco
• ISBN 10: 3322909433
• ISBN 13: 9783322909435
• Rilegatura: Copertina flessibile
• Numero di pagine: 228
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Germania