On the brachistochrone of a variable mass particle in general force fields

On the brachistochronic motion of a variable-mass mechanical system in general force fields

“…The characteristic of this numerical procedure is that in the shooting process the use of costate variables as the missing boundary conditions has been eliminated. The results obtained are an extension of the results from [34] to the case of variable-mass mechanical systems. Note that in [34] the particle mass has been taken as one of the state variables because the change in the particle mass was implicitly dependent on time t via a dependencė m =ṁ(m, v) of known form.…”

“…The results obtained are an extension of the results from [34] to the case of variable-mass mechanical systems. Note that in [34] the particle mass has been taken as one of the state variables because the change in the particle mass was implicitly dependent on time t via a dependencė m =ṁ(m, v) of known form. However, in this paper the particles' masses have not been taken as state variables because it was assumed that they change according to the specified relations (1) representing explicit dependencies of time t. The solution of the considered brachistochrone problem is based on fairly general assumptions with respect to potential and nonpotential forces acting on the mechanical system which make the results obtained sufficiently general and suitable for adaptation to some special cases (e.g.…”

“…Also, a certain number of references can be singled out [14,[28][29][30][31] where the solution of the classical brachistochrone problem (cycloid) was used with the aim of testing various numerical methods in solving nonlinear engineering optimization problems. References [32][33][34] consider the problem of brachistochronic motion of a variable-mass particle.…”

On the brachistochronic motion of mechanical systems with unilateral constraints

“…(9)), the brachistochronic motion of the considered system can be geometrically interpreted as the motion of a representative point M with respect to the Cartesian coordinate frame O 1 2 where O is the origin of the coordinate frame. Analogously to the case considered in Jeremić et al (2011Jeremić et al ( ),Šalinić (2009, the following kinematic relations can be introduced:…”

“…One group comprises the papers considering the problem of brachistochronic motion of a particle under the action of various types of forces, while the other group embraces the papers considering the problem of brachistochronic motion of mechanical systems. A detailed overview of literature dealing with the brachistochrone problem can be found inŠalinić (2009), Jeremić et al (2011). Regarding the problem considered in this paper, emphasis should be placed on those references where the classical Bernoulli's case is extended to the system of rigid bodies.…”