In this paper, a method is developed that results in guidelines for selecting the best Ordinary Differential Equation (ODE) solver and its parameters, for a class of nonlinear hybrid system were impacts are present. A monopod interacting compliantly with the ground is introduced as a new benchmark problem, and is used to compare the various solvers available in the widely used matlab ode suite. To provide result generality, the mathematical description of the hybrid system is brought to a dimensionless form, and its dimensionless parameters are selected in a range taken from existing systems and corresponding to different levels of numerical stiffness. The effect of error tolerance and phase transition strategy is taken into account. The obtained system responses are evaluated using solution speed and accuracy criteria. It is shown that hybrid systems represent a class of problems that cycle between phases in which the system of the equations of motion (EoM) is stiff (interaction with the ground), and phases in which it is not (flight phases); for such systems, the appropriate type of solver was an open question. Based on this evaluation, both general and case-specific guidelines are provided for selecting the most appropriate ODE solver. Interestingly, the best solver for a realistic test case turned out to be a solver recommended for numerically nonstiff ODE problems.
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November 2017
Research-Article
A Comparison of Ordinary Differential Equation Solvers for Dynamical Systems With Impacts
Spyridon Dallas,
Spyridon Dallas
Department of Mechanical Engineering,
National Technical University of Athens,
9 Heroon Polytechniou Street,
Athens 15780, Greece
e-mail: spyro.d.mechs@gmail.com
National Technical University of Athens,
9 Heroon Polytechniou Street,
Athens 15780, Greece
e-mail: spyro.d.mechs@gmail.com
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Konstantinos Machairas,
Konstantinos Machairas
Department of Mechanical Engineering,
National Technical University of Athens,
9 Heroon Polytechniou Street,
Athens 15780, Greece
e-mail: kmach@central.ntua.gr
National Technical University of Athens,
9 Heroon Polytechniou Street,
Athens 15780, Greece
e-mail: kmach@central.ntua.gr
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Evangelos Papadopoulos
Evangelos Papadopoulos
Mem. ASME
Department of Mechanical Engineering,
National Technical University of Athens,
9 Heroon Polytechniou Street,
Athens 15780, Greece
e-mail: egpapado@central.ntua.gr
Department of Mechanical Engineering,
National Technical University of Athens,
9 Heroon Polytechniou Street,
Athens 15780, Greece
e-mail: egpapado@central.ntua.gr
Search for other works by this author on:
Spyridon Dallas
Department of Mechanical Engineering,
National Technical University of Athens,
9 Heroon Polytechniou Street,
Athens 15780, Greece
e-mail: spyro.d.mechs@gmail.com
National Technical University of Athens,
9 Heroon Polytechniou Street,
Athens 15780, Greece
e-mail: spyro.d.mechs@gmail.com
Konstantinos Machairas
Department of Mechanical Engineering,
National Technical University of Athens,
9 Heroon Polytechniou Street,
Athens 15780, Greece
e-mail: kmach@central.ntua.gr
National Technical University of Athens,
9 Heroon Polytechniou Street,
Athens 15780, Greece
e-mail: kmach@central.ntua.gr
Evangelos Papadopoulos
Mem. ASME
Department of Mechanical Engineering,
National Technical University of Athens,
9 Heroon Polytechniou Street,
Athens 15780, Greece
e-mail: egpapado@central.ntua.gr
Department of Mechanical Engineering,
National Technical University of Athens,
9 Heroon Polytechniou Street,
Athens 15780, Greece
e-mail: egpapado@central.ntua.gr
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 4, 2016; final manuscript received May 24, 2017; published online September 7, 2017. Assoc. Editor: Stefano Lenci.
J. Comput. Nonlinear Dynam. Nov 2017, 12(6): 061016 (8 pages)
Published Online: September 7, 2017
Article history
Received:
December 4, 2016
Revised:
May 24, 2017
Citation
Dallas, S., Machairas, K., and Papadopoulos, E. (September 7, 2017). "A Comparison of Ordinary Differential Equation Solvers for Dynamical Systems With Impacts." ASME. J. Comput. Nonlinear Dynam. November 2017; 12(6): 061016. https://doi.org/10.1115/1.4037074
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