The General Problem Of The Motion Of Coupled Rigid Bodies About A Fixed Point

The General Problem of the Motion of Coupled Rigid Bodies about a Fixed Point

In the theory of motion of several coupled rigid bodies about a fixed point one can distinguish three basic ramifications. 1. The first, the so-called classical direction of investigations, is concerned with particular cases of integrability ot the equations of motion of a single rigid body about a fixed point,1 and with their geo metrical interpretation. This path of thought was predominant until the beginning of the 20th century and its most illustrious represen tatives are L. EULER (1707-1783), J L. LAGRANGE (1736-1813), L. POINSOT (1777-1859), S. V. KOVALEVSKAYA (1850-1891), and others. Chapter I of the present monograph intends to reflect this branch of investigations. For collateral reading on the general questions dealt with in this chapter the reader is referred to the following textbooks and reports: A. DOMOGAROV [1J, F. KLEIN and A. SOMMERFELD [11, 1 , 1 J, A. G. 2 3 GREENHILL [10J, A. GRAY [1J, R. GRAMMEL [4 J, E. J. ROUTH [21' 2 , 1 2 31' 32J, J. B. SCARBOROUGH [1J, and V. V. GOLUBEV [1, 2J.

The General Problem of the Motion of Coupled Rigid Bodies about a Fixed Point

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

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.