Optimal trajectories in brachistochrone problem with Coulomb friction
- Authors: Vondrukhov A.S.1,2, Golubev Y.F.1,2
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Affiliations:
- Moscow State University
- Keldysh Institute of Applied Mathematics
- Issue: Vol 55, No 3 (2016)
- Pages: 341-348
- Section: Optimal Control
- URL: https://journals.rcsi.science/1064-2307/article/view/219621
- DOI: https://doi.org/10.1134/S1064230716030163
- ID: 219621
Cite item
Abstract
A two-parameter family of optimal curves in the brachistochrone problem in the case of Coulomb friction is found. The problem is represented in the form of the standard time minimization control problem. The normal component of the support reaction is used as control. It turned out that the formula for the optimal control, which does not include adjoint variables, has a singularity at the zero motion velocity. A system of ordinary differential equations is derived for which the solution of the Cauchy initial value problem makes it possible to obtain optimal trajectories that have a vertical tangent at the initial point. The self-similarity property of such trajectories is proved. It is shown how this property can be used to obtain by scaling all optimal trajectories from the set of optimal trajectories with fixed initial conditions and different terminal slope angles of the tangent.
About the authors
A. S. Vondrukhov
Moscow State University; Keldysh Institute of Applied Mathematics
Author for correspondence.
Email: vondrukhov@gmail.com
Russian Federation, Moscow; Miusskaya pl. 4, Moscow, 125047
Yu. F. Golubev
Moscow State University; Keldysh Institute of Applied Mathematics
Email: vondrukhov@gmail.com
Russian Federation, Moscow; Miusskaya pl. 4, Moscow, 125047