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Meccanica
Published in: Meccanica 4-5/2017

25-03-2016

Contribution to the determination of the global minimum time for the brachistochronic motion of a holonomic mechanical system

Authors: Radoslav Radulović, Aleksandar Obradović, Slaviša Šalinić

Published in: Meccanica | Issue 4-5/2017

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Abstract

The problem of the brachistochronic motion of a holonomic scleronomic mechanical system is analyzed. The system moves in an arbitrary field of known potential forces. The problem is formulated as an optimal control task, where generalized speeds are taken as control variables. The problem considered is reduced to solving the corresponding two-point boundary-value problem (TPBVP). In order to determine the global minimal solution of the TPBVP, an appropriate numerical procedure based on the shooting method is presented. The global minimal solution represents the solution with the minimum time of motion. The procedure is illustrated by an example of determining the brachistochronic motion of a disk that performs plane motion in a vertical plane in a homogeneous field of gravity.
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Literature
1.
2.
McConnell AJ (1930) The brachistochronic motion of a dynamical system. Proc R Irish Acad 39A:31–48
3.
Bertolazzi E, Biral F, Da Lio M (2006) Symbolic numeric efficient solution of optimal control problems for multibody systems. J Comput Appl Math 185:404–421ADSMathSciNetCrossRefMATH
4.
5.
Dixon LCW, Biggs MC (1972) The advantages of adjoint control transformations when determining optimal trajectories by Pontryagin’s maximum principle. Areonaut J 76:169–174
6.
7.
Fahroo F, Ross IM (2001) Costate estimation by a Legendre pseudospectral method. J Guid Control Dyn 24:270–277ADSCrossRef
8.
Hull DG (2008) Initial Lagrange multipliers for the shooting method. J Guid Control Dyn 31:1490–1492ADSCrossRef
9.
Graichen K, Petit N (2008) A continuation approach to state and adjoint calculation in optimal control applied to the reentry problem. In: Proceedings of the 17th World congress the international federation of automatic control Seoul, Korea, July 6–11, pp 14307–14312
10.
Jiang F, Baoyin H, Li J (2012) Practical techniques for low-thrust trajectory optimization with homotopic approach. J Guid Control Dyn 35:245–258ADSCrossRef
11.
Park Ch, Guibout V, Scheeres D (2006) Solving optimal continuous thrust rendezvous problems with generating functions. J Guid Control Dyn 29:321–331ADSCrossRef
12.
Obradović A, Šalinić S, Jeremić O et al (2014) On the brachistochronic motion of a variable-mass mechanical system in general force fields. Math Mech Solids 19:398–410MathSciNetCrossRefMATH
13.
Mehrpouya MA, Shamsi M (2015) Gauss pseudospectral and continuation methods for solving two-point boundary value problems in optimal control theory. Appl Math Model 39:5047–5057MathSciNetCrossRef
14.
15.
Papastavridis JG (2002) Analytical mechanics. Oxford University Press, New YorkMATH
16.
Kelley H, Kopp RE, Moyer GH (1967) Singular extremals. In: Leitmann G (ed) Topics in optimization (mathematics in science and engineering, 31). Academic Press, New York, pp 63–101
17.
18.
Bryson AE, Ho YC (1975) Applied optimal control. Hemisphere, New York
19.
20.
21.
Strang G (1988) Linear algebra and its applications, 3rd edn. Harcourt Brace Jovanovich, San DiegoMATH
22.
Ruskeepaa H (2009) Mathematica ®Navigator: mathematics, statistics, and graphics, 3rd edn. Academic Press, BurlingtonMATH
23.
Hirsch MJ, Pardalos PM, Resende MGC (2009) Solving systems of nonlinear equations with continuous GRASP. Nonlinear Anal Real 10:2000–2006MathSciNetCrossRefMATH
24.
Song W, Wang Y, Li H-X et al (2015) Locating multiple optimal solutions of nonlinear equation systems based on multiobjective optimization. IEEE T Evolut Comput 19:414–431CrossRef
25.
Antunes ACB, Siguad C (2010) Controling nonholonomic Chaplygin systems. Braz J Phys 40:131–140ADSCrossRef
26.
27.
Šalinić S, Obradović A, Mitrović Z (2012) On the brachistochronic motion of mechanical systems with unilateral constraints. Mech Res Commun 45:1–6CrossRef
28.
Šalinić S, Obradović A, Mitrović Z et al (2013) On the brachistochronic motion of the Chaplygin sleigh. Acta Mech 224:2127–2141MathSciNetCrossRefMATH
29.
Yablonskii AA, Nikiforova VM (1966) Course of theoretical mechanics, vol 1, 3rd edn. Vischaya Shkola, Moscow (in Russian)
30.
31.
Zypman FR (2007) Instantaneous center of rotation and centrodes: background and new examples. Int J Mech Eng Educ 35:79–90CrossRef
Metadata
Title
Contribution to the determination of the global minimum time for the brachistochronic motion of a holonomic mechanical system
Authors
Radoslav Radulović
Aleksandar Obradović
Slaviša Šalinić
Publication date
25-03-2016
Publisher
Springer Netherlands
Published in
Meccanica / Issue 4-5/2017
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-016-0425-z

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