Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
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IssuesArchive of Issues2019-4pp.589-597

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I.E. Kaspirovich and R.G. Mukharlyamov, "On Constructing Dynamic Equations Methods with Allowance for Atabilization of Constraints," Mech. Solids. 54 (4), 589-597 (2019)
Year 2019 Volume 54 Number 4 Pages 589-597
DOI 10.3103/S0025654419040137
Title On Constructing Dynamic Equations Methods with Allowance for Atabilization of Constraints
Author(s) I.E. Kaspirovich (RUDN University (Peoples' Friendship University of Russia), ul. Miklukho-Maklaya, str. 6, Moscow, 117198 Russia, kaspirovich.ivan@mail.ru)
R.G. Mukharlyamov (RUDN University (Peoples' Friendship University of Russia), ul. Miklukho-Maklaya, str. 6, Moscow, 117198 Russia)
Abstract Based on the well-known methods of classical mechanics, the construction of dynamic equations for system using well-known constraint equations is associated with the accumulation of errors in the numerical solution and requires a certain modification to stabilize the constraints. The problem of constraint stabilization can be solved by changing the dynamic parameters of the system. It allows us to determine the Lagrange multipliers in the equations of motion and take into account possible deviations from the constraint equations. In systems with linear nonholonomic constraints, it is possible to express velocity projections in terms of the coordinate functions of the system. In this case, we can compose a system of second-order differential equations and present them in the form of Lagrange equations. Using the generalized Helmholtz conditions, one can compose the Lagrange equations with a dissipative function and ensure that the conditions for the stabilization of constraints are satisfied.
Keywords equations, constraints, stabilization, Helmholtz conditions, stability
Received 25 March 2018
Link to Fulltext https://link.springer.com/article/10.3103/S0025654419040137
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