Journal ArticleDOI
On the brachystochrone with dry friction
Reads0
Chats0
TLDR
In this paper, the problem of the brachystochrone with dry friction is governed by an autonomous set of highly non-linear ordinary differential equations, which contain a small parameter μ (the coefficient of friction), and using perturbation technique an approximate solution is constructed.Abstract:
The problem of the brachystochrone with dry friction is governed by an autonomous set of highly non-linear ordinary differential equations, which contain a small parameter μ (the coefficient of friction). Using perturbation technique an approximate solution is constructed.read more
Citations
More filters
Journal ArticleDOI
On the analytical solution of the brachistochrone problem in a non-conservative field
B. Vratanar,M. Saje +1 more
TL;DR: In this paper, a new approach to obtain an analytical solution of the brachistochrone problem in a non-conservative velocity-dependent frictional resistance field is presented, where geometrical and energy constraints are incorporated into a time functional through Lagrangian multipliers and the Euler-Lagrange equations in a natural coordinate system.
Journal ArticleDOI
Contribution to the brachistochrone problem with Coulomb friction
TL;DR: In this paper, the Coulomb friction of a particle which moves down a rough curve in a uniform gravitational field is considered, assuming that the initial velocity of the particle is different from zero.
Journal ArticleDOI
Brachistochrone on a surface with Coulomb friction
Vukman Čović,Miroslav Vesković +1 more
TL;DR: In this article, the problem of brachistochronic motion of a particle on a surface with the simultaneous action of gravity and Coulomb friction has been solved, and analytical solutions of the problem in special cases have been found.
Journal ArticleDOI
Brachistochrone for a rolling cylinder
TL;DR: In this paper, the authors considered the motion of a heavy homogeneous cylinder as a no-slip rolling along the desired curve and obtained a functional in the form of the total time of the cylinder rolling and solved the corresponding variational problem of minimizing this functional.
Journal ArticleDOI
On the brachistochrone of a variable mass particle in general force fields
TL;DR: It can be shown that these problems may be regarded as special cases of the brachistochrone problem formulated and solved in this paper under very general assumptions by means of optimal control theory.
Related Papers (5)
On the analytical solution of the brachistochrone problem in a non-conservative field
B. Vratanar,M. Saje +1 more