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Title: Brachistochrone with limited reaction of constraint in an arbitrary force field
Authors: Šalinić, Slaviša
Obradovic, Aleksandar
Mitrović Z.
Rusov S.
Journal: Nonlinear Dynamics
Issue Date: 1-Jan-2012
Abstract: The paper considers brachistochronic motion of a particle along a curve y=y(x) in an arbitrary force field in the vertical plane of Cartesian coordinate system. The curve is treated as a bilateral or unilateral constraint that can be smooth or rough. The projection of the reaction force of the curve onto the normal to the curve is confined to the fixed limits. A control variable u is given as the second derivative of the function y(x) relative to the horizontal coordinate x of the particle, i.e., u=d 2 y/dx 2. Applying Pontryagin's maximum principle and singular optimal control theory, the problem is reduced to numerical solving of the corresponding two-point boundary value problem. The procedure based on the shooting method is used to solve the boundary value problem. Two examples with friction forces of the viscous friction and Coulomb friction type have been solved. © 2011 Springer Science+Business Media B.V.
Type: Article
DOI: 10.1007/s11071-011-0258-1
ISSN: 0924090X
SCOPUS: 84861746884
Appears in Collections:Faculty of Mechanical and Civil Engineering, Kraljevo
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