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research-article

A Comparison of ODE Solvers for Dynamical Systems with Impacts

[+] Author and Article Information
Spyridon Dallas

Department of Mechanical Engineering National Technical University of Athens 9 Heroon Polytechniou Str. 15780 Athens, Greece
spyro.d.mechs@gmail.com

Konstantinos Machairas

Department of Mechanical Engineering National Technical University of Athens 9 Heroon Polytechniou Str. 15780 Athens, Greece
kmach@central.ntua.gr

Evangelos Papadopoulos

Department of Mechanical Engineering National Technical University of Athens 9 Heroon Polytechniou Str. 15780 Athens, Greece
egpapado@central.ntua.gr

1Corresponding author.

ASME doi:10.1115/1.4037074 History: Received December 04, 2016; Revised May 24, 2017

Abstract

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 systems with impacts. 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 with impacts 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.

Copyright (c) 2017 by ASME
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