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Evolution of Motions of a Rigid Body About its Center of Mass

verfasst von: Felix L. Chernousko, Leonid D. Akulenko, Dmytro D. Leshchenko

Verlag: Springer International Publishing

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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Über dieses Buch

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 approach based on the averaging procedure is applicable to bodies with arbitrary ellipsoids of inertia. Action of various perturbation torques, both external (gravitational, aerodynamical, solar pressure) and internal (due to viscous fluid in tanks, elastic and visco-elastic properties of a body) is considered in detail. The book can be used by researchers, engineers and students working in attitude dynamics of spacecraft.

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Inhaltsverzeichnis

Frontmatter

Chapter 1. The Foundations of Dynamics of a Rigid Body with a Fixed Point

Abstract

Consider a rigid body moving about a fixed point O. The position of the rigid body in space is determined at each moment of time by the position of the moving coordinate system Oxyz connected with the body relative to the fixed coordinate system Ox ₁ y ₁ z ₁. To determine the body position, three independent (among themselves) parameters corresponding to the number of degrees of freedom of the body are introduced. Let us consider one of the most common ways of determining orientation of a rigid body using the Euler angles [1–4]. The plane Oxy intersects with planeOx ₁ y ₁ along the line ON, called the line of nodes. Figure 1.1 shows the angle ψ of precession as the angle between the axis Ox ₁ and the line of nodes ON, the angle of nutation θ as the angle between the axes Oz and Oz ₁, and the angle φ of proper rotation as the angle between the line of nodes ON and the axis Ox.

Felix L. Chernousko, Leonid D. Akulenko, Dmytro D. Leshchenko

Chapter 2. Motion of a Rigid Body by Inertia. Euler’s Case

Abstract

In Euler’s case, the principal moment of external forces acting on a rigid body relative to a fixed point is equal to zero \( {\mathbf{L}}_0^e=0 \). The dynamic Euler’s equations (1.27) assume the form:

Felix L. Chernousko, Leonid D. Akulenko, Dmytro D. Leshchenko

Chapter 3. Lagrange’s Case

Abstract

Suppose that the ellipsoid of inertia of a rigid body relative to a fixed point O is an ellipsoid of revolution, i.e., A ₁ = A ₂, whereas the center of gravity of the body lies on the axis of dynamic symmetry of the body. Let us introduce the moving and fixed systems of coordinates Oxyz and Ox ₁ y ₁ z ₁ in the following way (Fig. 3.1):

Felix L. Chernousko, Leonid D. Akulenko, Dmytro D. Leshchenko

Chapter 4. Equations of Perturbed Motion of a Rigid Body About Its Center of Mass

Abstract

The subject of this book is the investigation of perturbed motions of a rigid body about its center of mass under the action of torques of various physical nature. If the body is not acted upon by the internal or external torques, then it performs a certain motion which is called unperturbed. As an unperturbed motion, one usually considers the motion in the case of Euler or Lagrange. In real conditions, the body is acted upon by the perturbation moments of internal or external forces, in particular, gravitation forces, the forces of the medium resistance and the internal dissipative forces.

Felix L. Chernousko, Leonid D. Akulenko, Dmytro D. Leshchenko

Chapter 5. Perturbation Torques Acting upon a Rigid Body

Abstract

This chapter examines the internal and external torques of various physical natures, which can act as perturbation torques during the motion of a rigid body relative to the center of mass. The dynamics of rigid bodies under the influence of these torques will be investigated in subsequent chapters.

Felix L. Chernousko, Leonid D. Akulenko, Dmytro D. Leshchenko

Chapter 6. Motion of a Satellite About Its Center of Mass Under the Action of Gravitational Torque

Abstract

The work [1] considers two cases of motion of a satellite under the action of gravitational torques when the presence of a small parameter allows applying the averaging method and obtaining asymptotic solutions.

Felix L. Chernousko, Leonid D. Akulenko, Dmytro D. Leshchenko

Chapter 7. Motion of a Rigid Body with a Cavity Filled with a Viscous Fluid

Abstract

In this chapter, we consider the motion about the center of mass of a rigid body with a cavity filled with a viscous fluid. It is assumed that the viscosity of the fluid is sufficiently high, so the corresponding Reynolds number is small. The torques acting on the body by the viscous fluid in the cavity are determined by the method developed in [1–3] and described in Sect. 5.3.

Felix L. Chernousko, Leonid D. Akulenko, Dmytro D. Leshchenko

Chapter 8. Evolution of Rotations of a Rigid Body in a Medium

Abstract

The scheme of asymptotic solution suggested in Sects. 4.6 and 6.2 is applicable not only to the problems of motion of a satellite relative to its center of mass but also to other problems of fast motion of a rigid body. In Sect. 8.1, we consider fast motion of a rigid body about a fixed point [1].

Felix L. Chernousko, Leonid D. Akulenko, Dmytro D. Leshchenko

Chapter 9. Motion of a Rigid Body with Internal Degrees of Freedom

Abstract

In Sect. 9.1, following [1], we study the problems of motion of a free rigid body carrying a movable mass connected with the body by an elastic coupling in the presence of viscous friction. The cases of complete dynamic symmetry of the body and the case of the axially dynamically symmetric body are considered.

Felix L. Chernousko, Leonid D. Akulenko, Dmytro D. Leshchenko

Chapter 10. Influence of the Torque Due to the Solar Pressure upon the Motion of a Sun Satellite Relative to Its Center of Mass

Abstract

In Sect. 10.1, we describe the coordinate systems used in the sequel. We present a phenomenological formula for the torque L due to the light pressure acting on a Sun satellite. The equations of the perturbed motion of the satellite in the presence of the force function are written. We note some results obtained in [1, 2] in the study of motion of a dynamically nonsymmetric or symmetric satellite relative to its center of mass under the action of the light pressure torque.

Felix L. Chernousko, Leonid D. Akulenko, Dmytro D. Leshchenko

Chapter 11. Perturbed Motions of a Rigid Body Close to Lagrange’s Case

Abstract

In Sect. 11.1, we describe an averaging procedure for slow variables of a perturbed motion of a rigid body, where the motion is close to Lagrange’s case in the first approximation [1]. It turns out that a number of applied problems admit averaging over the nutation angle θ.

Felix L. Chernousko, Leonid D. Akulenko, Dmytro D. Leshchenko

Titel: Evolution of Motions of a Rigid Body About its Center of Mass
verfasst von: Felix L. Chernousko
Leonid D. Akulenko
Dmytro D. Leshchenko
Copyright-Jahr: 2017
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-53928-7
Print ISBN: 978-3-319-53927-0
DOI: https://doi.org/10.1007/978-3-319-53928-7

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