On the brachistochrone of a variable mass particle in general force fields
| Autor: | Olivera Jeremić, Zoran Mitrović, Aleksandar Obradovic, Slaviša Šalinić |
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| Rok vydání: | 2011 |
| Předmět: |
Variables
media_common.quotation_subject 010102 general mathematics Mathematical analysis 02 engineering and technology Optimal control 01 natural sciences law.invention Computer Science Applications 020303 mechanical engineering & transports Shooting method 0203 mechanical engineering law Modeling and Simulation Modelling and Simulation Resistance force Cartesian coordinate system Boundary value problem 0101 mathematics Hamiltonian (control theory) Brachistochrone curve media_common Mathematics |
| Zdroj: | Mathematical and Computer Modelling. 54(11-12):2900-2912 |
| ISSN: | 0895-7177 |
| DOI: | 10.1016/j.mcm.2011.07.011 |
| Popis: | The problem of the brachistochronic motion of a variable mass particle is considered. The particle moves through a resistant medium in the field of arbitrary active forces. Beginning from these general assumptions, and applying Pontryagin’s minimum principle along with singular optimal control theory, a corresponding two-point boundary value problem is obtained and solved. The solution proposed involves an appropriate numerical procedure based upon the shooting method. In this numerical procedure, the evaluation of ranges for unknown values of costate variables is avoided by the choice of a corresponding Cartesian coordinate of the particle as an independent variable. A numerical example assuming the resistance force proportional to the square of the particle speed is presented. A review of existing results for related problems is provided, and 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. |
| Databáze: | OpenAIRE |
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