Grigory Rozenblat
64, Leningradskyi prospekt, 125319, Moscow
The Moscow State Automobile and Road Technical University
Publications:
Zhuravlev V. F., Rozenblat G. M.
Estimates of Solutions During Motion of the Euler –Poinsot Top and Explanation of the Experiment with Dzhanibekov’s Nut
2020, Vol. 16, no. 3, pp. 517-525
Abstract
This paper presents secure upper and lower estimates for solutions to the equations of
rigid body motion in the Euler case (in the absence of external torques). These estimates are
expressed by simple formulae in terms of elementary functions and are used for solutions that
are obtained in a neighborhood of the unstable steady rotation of the body about its middle
axis of inertia. The estimates obtained are applied for a rigorous explanation of the flip-over
phenomenon which arises in the experiment with Dzhanibekov’s nut.
|
Rozenblat G. M.
A method for determination of the parameters of motion of a top that moves without bouncing on a smooth plane
2008, Vol. 4, No. 1, pp. 87-98
Abstract
The problem of motion of an axisymmetric rigid body on a horizontal plane in the presence of gravity is considered. The body touches the plane at one point, and the plane is assumed to be perfectly smooth. In the already-known and integrable case of symmetric body the normal reaction force exerted by the plane onto the body is calculated and its sign is examined. The condition that the body remains in contact with the plane is that the reaction is positive because the constraint at the point of contact is assumed to be unilateral. In some cases a comparatively trivial analytical representation (a polynomial of degree two) for the reaction force is obtained which allows determination of the initial conditions and the body’s parameters for the body to remain in contact with the plane.
|
Rozenblat G. M.
On the motion of a two-dimensional rigid body on a rough straight line
2006, Vol. 2, No. 3, pp. 293-306
Abstract
We study the motion (rolling motion) of a flat plate whose boundary is an arbitrary convex curve along a straight line. During the motion the plate is always in contact with the supporting line and subject to a dry friction. Plus, the plate is acted on by an arbitrary plane system of forces and at the point of contact only the unilateral constraint is assumed. All possible transitions from a rolling motion with slipping to a pure rolling without slipping and vice versa are classified. Necessary conditions for the plate to remain in contact with the line are obtained. The results obtained are used to study 1) the motion of a non-uniform circular disk, subject to gravity, on a rough horizontal straight line in the vertical plane and 2) the motion of a slender rod, subject to gravity, on a rough straight line.
|