Construction of equations of dynamics of a given structure based on equations of program constraints

R. G. Mukharlyamov

RUDN University, Moscow, Russia

Abstract: We consider the problem of constructing a system of differential equations from a given set of constraint equations and reducing them to the form of Lagrange equations with dissipative forces that ensure stabilization of the constraints. We determine the dissipative function from the equations of constraint disturbances. We use modified Helmholtz conditions to represent differential equations in the form of Lagrange equations. We give the solution of the Bertrand problem of determining the central force under the action of which a material point performs stable motion along a conic section.

Keywords: constraint equations, Lagrange equation, dissipative function, Helmholtz conditions, Bertrand problem.

UDC: 519.6

DOI: 10.22363/2413-3639-2024-70-3-428-440

 English version: Journal of Mathematical Sciences, 2024, 287:4, 609–619