Geodesic
Construction of equations of dynamics of a given structure based on equations of program constraints
Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 70 (2024) no. 3, pp. 428-440

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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.
Mots-clés : constraint equations, Lagrange equation, Bertrand problem.
Keywords: dissipative function, Helmholtz conditions 
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     title = {Construction of equations of dynamics of a given structure based on equations of program constraints},
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R. G. Mukharlyamov. Construction of equations of dynamics of a given structure based on equations of program constraints. Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 70 (2024) no. 3, pp. 428-440. http://geodesic.mathdoc.fr/item/CMFD_2024_70_3_a6/