Evolution of motions of a rigid body about its center of mass

• Main Authors: Chernousʹko, F. L. (Author), Akulenko, L. D. (Author), Leshchenko, Dmytro D. (Author)
• Format: Electronic eBook
• Language: English
• Published: Cham, Switzerland : Springer, 2017.
• Subjects: Center of mass.; Dynamics, Rigid.; elektronické knihy; electronic books
• ISBN: 9783319539287; 9783319539270
• Physical Description: 1 online resource (xxxviii, 241 pages) : illustrations

The book presents a unified and well-developed approach to the dynamics of angular motions of rigid bodies subjected to perturbation torques of different physical nature. It contains both the basic foundations of the rigid body dynamics and of the asymptotic method of averaging. The rigorous approac...

Table of Contents:

• Preface; Survey of Literature; References; About this Book; Contents; Chapter 1: The Foundations of Dynamics of a Rigid Body with a Fixed Point; 1.1 Orientation of a Body: The Euler Angles; 1.2 Geometry of Mass: Moments of Inertia; 1.3 Theorem of Change of Angular Momentum; 1.4 Dynamic Eulerś Equations; 1.5 Kinematic Eulerś Equations: Direction Cosines; 1.6 Equations of Motion of a Heavy Rigid Body About a Fixed Point; References; Chapter 2: Motion of a Rigid Body by Inertia. Eulerś Case; 2.1 First Integrals; 2.2 Basic Formulas for the Jacobian Elliptic Functions.
• 2.3 Integration of Dynamic Eulerś Equations: Analysis of the Motion2.4 Particular Cases (Regular Precession, Permanent Rotations); References; Chapter 3: Lagrangeś Case; 3.1 Integration of the Equations of Motion and Analysis of Motion; 3.2 Regular Precession; 3.3 Fast Spinning Top; References; Chapter 4: Equations of Perturbed Motion of a Rigid Body About Its Center of Mass; 4.1 The Concept of a Perturbed Motion; 4.2 Basic Concepts of the Averaging Method: Systems in a Standard Form and Systems with Fast Rotating Phase; 4.3 Systems Containing Slow and Fast Motions.
• 4.4 Higher-Order Averaging in Systems with Fast and Slow Phases4.5 Equations of Perturbed Motion of a Rigid Body Close to Eulerś Case; 4.6 Equations of Perturbed Motion of a Satellite About Its Center of Mass; 4.7 Procedure of Averaging for a Body with Moments of Inertia Close to One Another; 4.8 Equations of Perturbed Rotational Motion of a Rigid Body Close to Lagrangeś Case; 4.8.1 General Case; 4.8.2 The Case Where the Projections of the Perturbation Torque Vector Are of Different Orders of Smallness; 4.8.3 Perturbation Torques Are Small Compared to the Restoring Ones; References.
• Chapter 5: Perturbation Torques Acting upon a Rigid Body5.1 Gravitational Torques Acting upon a Satellite; 5.2 Rigid Body in a Resistant Medium; 5.3 Rigid Body with a Cavity Filled with the Fluid of High Viscosity; 5.4 Case of Moving Masses Connected to the Body by Elastic Couplings with Viscous Friction; 5.5 Body with Elastic and Dissipative Elements; 5.6 Viscoelastic Solid Body; 5.7 Influence of a Moving Mass Connected to the Body by an Elastic Coupling with Quadratic Friction; 5.8 Torque Due to the Solar Pressure; References.
• Chapter 6: Motion of a Satellite About Its Center of Mass Under the Action of Gravitational Torque6.1 Motion of a Triaxial Satellite with Moments of Inertia Close to One Another; 6.2 Fast Rotations of a Satellite with a Triaxial Ellipsoid of Inertia; 6.3 Resonance Phenomena in the Planar Motion of a Satellite About Its Center of Mass; References; Chapter 7: Motion of a Rigid Body with a Cavity Filled with a Viscous Fluid; 7.1 Equations of Motion of a Body with a Viscous Fluid in a Cavity; 7.2 Planar Motion of a Pendulum with a Viscous Fluid.