Spatial topographical systems of Poincaré and comparison systems

Abstract

The differential collision cross section for the scattering of water molecules has been measured up to 25 degrees at 20 x erg relative energy. The small angle behaviour of the cross section cannot be described in terms of elastic scattering between fast (nor slow) rotating dipoles. The Lennard-Jones (12-6) potential that best describes the wide angle portion of the cross section has a well depth of 5.8 x erg.

Stability of a rigid body translating in a resisting medium

“…Theorem 4. Function (6.12) is a Lyapunov (Chetaev) function for system (6.11), i.e., by virtue of (6.11), its derivative in the neighborhood of the origin is negative definite for s ¢ < R h ( ) 0 1 [15,16]). Indeed, the derivative of function (7.4) by virtue of (7.1)-(7.3) is given by and it is a negative definite function in a sufficiently small neighborhood of the origin.…”

“…The other portion of the body surface can be placed in a volume bounded by the surface of the jet stalling at the edge of the plate and is not affected by the medium. Conditions are similar when the body enters water [4,5,7,12,14,16]. The gravity is assumed negligible compared with the resistance of the medium (see also [20][21][22][23][24]).…”

“…Since the nonlinear analysis is complex, the initial stage of such a study disregards the dependence of the moment of force of the medium on the angular velocity of the body and considers the dependence on the angle of attack alone [9,11,16].…”

“…Studies of the plane and spatial models describing the interaction of a rigid body and a medium (in the presence or absence of an additional follower force) have established sufficient stability conditions for translational motion, which is a key type of motion. It was shown that there are conditions under which stable or unstable self-oscillatory motion is possible.Since the nonlinear analysis is complex, the initial stage of such a study disregards the dependence of the moment of force of the medium on the angular velocity of the body and considers the dependence on the angle of attack alone [9,11,16].Of practical importance is the stability analysis of the so-called unperturbed (translational) motion such that the velocities of points of the body are perpendicular to the plate (cavitator).All the results obtained under this elementary assumption allows concluding that there no conditions under which the systems would have solutions describing angular finite-amplitude oscillations of the body.The present paper is the next stage in the study of a moving rigid body interacting with the medium only by the flat front area (plate). The force exerted by the medium is found using the properties of a quasistationary jet flow [9].…”

Spatial motion of a rigid body in a resisting medium

“…x y z 0 0 0 , q, y, j) are cyclic, which reduces the order of the dynamic system [10][11][12][13][14][15].…”