On the brachistochronic motion of mechanical systems with unilateral constraints

Šalinić, Slaviša; Obradović, Aleksandar; Mitrović, Zoran

doi:10.1016/j.mechrescom.2012.06.006

Cited by 5 publications

(5 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…with constrained motion (1), we have presented the procedure of generating differential equations of motion (4) and (5), based on the general theorems of dynamics [9]. The formulated brachistochrone problem, with a corresponding choice of the equations of state (8), was solved, in this case, as the simplest problem of optimal control. Applying the Pontryagin maximum principle [11] and [12], the problem of optimal control was solved (see Fig.…”

Section: Discussionmentioning

confidence: 99%

“…The results obtained in [6] were extended in [8], where the brachistochronic motion of a mechanical system with unilateral constraints was considered. This paper, using the example of a nonholonomic mechanical system with limited reactions of constraints, presents the procedure of creating the differential equations of motion where both reactions of nonholonomic constraints and control forces figure, based on the general theorems of dynamics [9].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

10.5937/fmet1403199r = Analysis of the minimum required coefficient of sliding friction at brachistochronic motion of a nonholonomic mechanical system

Radulović¹,

Obradović²,

Jeremić³

2014

FME Transaction

View full text Add to dashboard Cite

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

10.5937/fmet1403199r = Analysis of the minimum required coefficient of sliding friction at brachistochronic motion of a nonholonomic mechanical system

Radulović¹,

Obradović²,

Jeremić³

2014

FME Transaction

View full text Add to dashboard Cite

“…x y φ and ξ , so that the system starting from the initial state on manifolds (14), moves to the end state on manifolds (15), with unchanged value of mechanical energy (12), in a minimum time.…”

Section: Brachistochronic Motion As the Problem Of Optimal Controlmentioning

confidence: 99%

“…x y λ , λ λ   , φ λ and ξ λ are coordinates of the conjugate vector, where it can be taken that 0 1 λ   , while μ is a multiplier corresponding to the relation (12). Taking into account the boundary conditions (14) and (15), as well as the fact that time does not figure explicitly in equations of state (13), the defined problem of optimal control can be solved by a straightforward application of Theorem 3, that is, Theorem 1 [1].…”

Section: Brachistochronic Motion As the Problem Of Optimal Controlmentioning

confidence: 99%

Analysis the brachistochronic motion of a mechanical system with nonlinear nonholonomic constraint

Radulović¹,

Zeković²,

Lazarević³

et al. 2014

FME Transaction

View full text Add to dashboard Cite

This paper analyzes the problem of brachistochronic planar motion of a mechanical system with nonlinear nonholonomic constraint. The nonholonomic system is represented by two Chaplygin blades of negligible dimensions, which impose nonlinear constraint in the form of perpendicularity of velocities. The brachistrochronic planar motion is considered, with specified initial and terminal positions, at unchanged value of mechanical energy during motion. Differential equations of motion, where the reactions of nonholonomic constraints and control forces figure, are obtained on the basis of general theorems of mechanics. Here, this is more convenient to use than some other methods of analytical mechanics applied to nonholonomic mechanical systems, where a subsequent physical interpretation of the multipliers of constraints is required. The formulated brachistochrone problem, with adequately chosen quantities of state, is solved as simple a task of optimal control as possible in this case by applying the Pontryagin maximum principle. The corresponding two-point boundary value problem of the system of ordinary nonlinear differential equations is obtained, which has to be numerically solved. Numerical procedure for solving the two-point boundary value problem is performed by the method of shooting. On the basis of thus obtained brachistochronic motion, the active control forces, along with the reactions of nonholonomic constraints, are defined. Using the Coulomb friction laws, a minimum required value of the coefficient of sliding friction is defined, so that the considered system is moving in accordance with nonholonomic bilateral constraints

show abstract

“…In the paper [8] Šalinić, Obradović, and Mitrović considered the case of brachistochronic motion of mechanical system with two degrees of freedom in which ideal bilateral constraints and one unilateral constrain with Coulomb friction are imposed on the system.…”

Section: Introductionmentioning

confidence: 99%

On brachistochronic motion of a multibody system with two degrees of freedom with real constraints

Djuric¹

2015

FME Transaction

View full text Add to dashboard Cite

The paper considers a case of brachistrochronic motion of the mechanical system in the field of conservative forces, subject to the action of constraints with Coulomb friction. In this case an analogy is made between the two approaches of solving this problem of the mechanical system with two degrees of freedom. The mathematical model used to compute the brachistohrone in this special case of the multibody system with two deegres of freedom is based on varational calculus. The complete analogy is made with a solution in relation to material point.

show abstract

On the brachistochronic motion of mechanical systems with unilateral constraints

Cited by 5 publications

References 18 publications

10.5937/fmet1403199r = Analysis of the minimum required coefficient of sliding friction at brachistochronic motion of a nonholonomic mechanical system

10.5937/fmet1403199r = Analysis of the minimum required coefficient of sliding friction at brachistochronic motion of a nonholonomic mechanical system

Analysis the brachistochronic motion of a mechanical system with nonlinear nonholonomic constraint

On brachistochronic motion of a multibody system with two degrees of freedom with real constraints

Contact Info

Product

Resources

About