A theory of systems with unilateral constraints. (English. Russian original) Zbl 0925.70143

J. Appl. Math. Mech. 59, No. 4, 505-512 (1995); translation from Prikl. Mat. Mekh. 59, No. 4, 531-539 (1995).
Summary: 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.


70F20 Holonomic systems related to the dynamics of a system of particles
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[1] Painlevé, P., Leçons sur le frottement, (1895), Gauthier-Villars Paris · JFM 26.0781.01
[2] Rubin, H.; Ungar, P., Motion under a strong constraining force, Comm. pure appl. math., 10, 1, 65-87, (1957) · Zbl 0077.17401
[3] Kozlov, V.V.; Neishtadt, A.I., On the realization of holonomic constraints, Prikl. mat. mekh., 54, 5, 858-861, (1990)
[4] Novozhilov, I.V., Fractional analysis, (1991), Izd. Mosk. Gos. Univ Moscow · Zbl 0747.34032
[5] Baumgarte, J., Stabilization of constraints and integrals of motion in dynamical systems, Computer meth. appl. mech. engng, 1, 1, 1-16, (1972) · Zbl 0262.70017
[6] Kozlov, V.V., A constructive method for substantiating the theory of systems with non-retentive constraints, Prikl. mat. mekh., 52, 6, 833-894, (1988)
[7] Kozlov, V.V.; Treshchev, D.V., Billiards. A genetic introduction to the dynamics of systems with impacts, () · Zbl 0751.70009
[8] Kozlov, V.V., On impact with friction, Izv. akad. nauk SSSR. MTT, 6, 54-60, (1989)
[9] Deryabin, M.V., On the realization of non-retentive constraints, Prikl. mat. mekh., 58, 6, 136-140, (1994)
[10] Rashevskii, P.K., Riemannian geometry and tensor analysis, (1967), Nauka Moscow · Zbl 0186.06502
[11] Karapetyan, A.V., On the realization of non-holonomic constraints by forces of viscous friction and the stability of celtic rocks, Prikl. mat. mekh., 45, 1, 42-51, (1981)
[12] Brendelev, V.N., On the realization of constraints in non-holonomic mechanics, Prikl. mat. mekh., 45, 3, 481-487, (1981) · Zbl 0496.70026
[13] Vasil’yeva, A.B.; Butuzov, V.F., Asymptotic expansions of solutions of singularly perturbed equations, (1973), Nauka Moscow · Zbl 0364.34028
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