A new approach for the determination of the global minimum time for the Chaplygin sleigh brachistochrone problem

Radulović, Radoslav; Šalinić, Slaviša; Obradović, Aleksandar; Rusov, Srdjan

doi:10.1177/1081286516637234

Cited by 3 publications

(3 citation statements)

References 19 publications

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“…The solutions of the system are at the intersection of the curves whose implicit equations are the system equations. As an alternative to numerical calculation this graphical method was also proposed in [18] and [19]. The solution of the considered system of algebraic equations could be geometrically represented in the form of intersection of the corresponding surfaces [19].…”

Section: Virtual Displacements and Static Equilibrium In Generalized mentioning

confidence: 99%

“…As an alternative to numerical calculation this graphical method was also proposed in [18] and [19]. The solution of the considered system of algebraic equations could be geometrically represented in the form of intersection of the corresponding surfaces [19]. The implementation of the method of crossing of the curves is achieved, same as in [20], by using the built-in ContourPlot Mathematica function.…”

Section: Virtual Displacements and Static Equilibrium In Generalized mentioning

confidence: 99%

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Analysis of the motion and stability of the holonomic mechanical system in the arbitrary force field

Vesović¹,

Petrović²,

Radulović³

2021

FME Transactions

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In order to give an insight into the work of the machine before the production and assembly and to obtain good analysis, this paper presents detailed solutions to the specific problem occured in the field of analytical mechanics. In addition to numerical procedures in the paper, a review of the theoretical foundations was made.Various types of analysis are very common in mechanical engineering, due to the possibility of an approximation of complex machines. For the proposed system, Lagrange's equations of the first kind, covariant and contravariant equations, Hamiltons equations and the generalized coordinates, as well as insight in Coulumb friction force are provided.Also, the conditions of static equilibrium are solved numerically and using intersection of the two curves. Finally, stability of motion for the disturbed and undisturbed system was investigated.

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Section: Virtual Displacements and Static Equilibrium In Generalized mentioning

confidence: 99%

Section: Virtual Displacements and Static Equilibrium In Generalized mentioning

confidence: 99%

Analysis of the motion and stability of the holonomic mechanical system in the arbitrary force field

Vesović¹,

Petrović²,

Radulović³

2021

FME Transactions

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“…(3.6)-(3.8), consists in determining the controls 1 and 2 and the state variables , , and corresponding to them, so that the disk starting from the initial position in which one has: Note that for the initial and terminal instants of motion, from the relation (3.9) it follows that | | 1 and | | 1. In this manner, using the built-in functions NDSolve and First in the Mathematica program package [34], the following dependencies can be established in a numerical form: of determining the global minimum time of the brachistochronic motion of mechanical systems can be found in more detail in [35,36]. Further, it is noticeable from Fig.…”

Section: The Brachistochronic Rolling Of the Disk Under The Sufficienmentioning

confidence: 99%

The brachistochronic motion of a vertical disk rolling on a horizontal plane without slip

Obradović

Šalinić²,

Radulović

2017

Theor appl mech (Belgr)

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This paper deals with the brachistochronic motion of a thin uniform disk rolling on a horizontal plane without slip. The problem is formulated and solved within the frame of the optimal control theory. The brachistochronic motion of the disk is controlled by three torques. The possibility of the realization of the brachistochronic motion found in presence of Coulomb dry friction forces is inspected. Also, the influence of values of the coefficient of dry friction on the structure of the extremal trajectory is analyzed. Two illustrative numerical examples are provided.

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Realization of the brachistochronic motion of Chaplygin sleigh in a vertical plane with an unilateral nonholonomic constraint

Obradovic,

Cherkasov,

Milicic

et al. 2023

Theor appl mech (Belgr)

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The paper considers the procedure for determining the brachistochronic motion of the Chaplygin sleigh in a vertical plane, where the blade is such that it prevents the motion of the contact point in one direction only. The position of the sleigh mass center and orientation at the final positions is specified, as well as the initial value of mechanical energy. The simplest formulation of a corresponding optimal control problem is given and it is solved by applying Pontryagin?s maximum principle. For some cases, analytical solutions of differential equations of the two-point boundary value problem (TPBVP) of the maximum principle were found. Numerical integration was carried out for other cases using the shooting method, where the assessment of missing terminal conditions was given and it was shown that the solution obtained represents the global minimum time for the brachistochronic motion. The method of the brachistochronic motion by means of a single holonomic and a single unilateral nonholonomic mechanical constraint is presented.

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A new approach for the determination of the global minimum time for the Chaplygin sleigh brachistochrone problem

Cited by 3 publications

References 19 publications

Analysis of the motion and stability of the holonomic mechanical system in the arbitrary force field

Analysis of the motion and stability of the holonomic mechanical system in the arbitrary force field

The brachistochronic motion of a vertical disk rolling on a horizontal plane without slip

Realization of the brachistochronic motion of Chaplygin sleigh in a vertical plane with an unilateral nonholonomic constraint

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