On effect of “emerging” of a heavy rigid body in a fluid
Mechanics of Solids, 2002, vol. 37, no. 1, pp. 54-59
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The fall of a heavy rigid body in unbounded volume of an ideal fluid is considered. The fluid performs an irrotational motion and rests at infinity. It is assumed that the wider side of the body is horizontal at the initial time instant at which a velocity is communicated to the body in the horizontal direction. Then at the next time instants the body starts descending. However, if the associated mass of the body in the transverse direction is sufficiently large, the body then sharply comes to the surface with his narrower side ahead and rises to the height exceeding that at the initial time instant. The analysis of the surfacing effect involves the expansion of the solutions of Kirchhoff's equations into series in powers of time and the evaluation of the coefficients of these series by means of Cauchy majorants.
Deryabin M. V., Kozlov V. V., On effect of “emerging” of a heavy rigid body in a fluid, Mechanics of Solids, 2002, vol. 37, no. 1, pp. 54-59
On the theory of systems with unilateral constraints
Journal of Applied Mathematics and Mechanics, 1995, vol. 59, no. 4, pp. 505–512
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The realization of a unilateral constraint is considered in a situation in which the stiffness and coefficient of viscosity and the added masses tend to infinity simultaneously in a consistent manner. The main result is that limiting motions exist, which are identical on the boundary with the motions of a holonomic system with fewer degrees of freedom. However, a special effect, not present in the classical model, occurs here, namely, a delay in the time at which the constraint is released.
Deryabin M. V., Kozlov V. V., On the theory of systems with unilateral constraints, Journal of Applied Mathematics and Mechanics, 1995, vol. 59, no. 4, pp. 505–512