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ModiaMath.jl Documentation

ModiaMath provides a simulation engine and other mathematical utilities for packages Modia and Modia3D that are used to model physical systems such as electrical circuits, robots, or vehicles. The recommended way is to use ModiaMath via Modia or Modia3D. However, ModiaMath is self-contained and can be also used without Modia/Modia3D.

The central part of ModiaMath is a simulation engine to solve implicit index one Differential Algebraic Equations (DAEs) with and without time and state events. The theory is partially described in (Otter/Elmqvist, 2017). In particular it is shown, that a large class of DAEs can be transformed automatically to this form (including multibody systems with kinematic loops). As integrator currently IDA of the Sundials integrator suite is used (via the Julia Sundials interface package). It is planned to adapt ModiaMath to Julia package DifferentialEquations and use IDA and other appropriate integrators via this package in the future.

Additionally, ModiaMath provides functions to perform plotting in a convenient way, to generate and use rotation matrices and quaternions for kinematic transformations in 3D, and to provide an infrastructure for DAE variables as needed by Modia3D.

Installation

The package is registered in METADATA.jl and can be installed in the following way (Julia >= 1.0 is required):

julia> ]add ModiaMath

ModiaMath uses PyPlot for plotting. If PyPlot is not available in your current Julia environment an information message is printed and all ModiaMath.plot(..) calls are ignored. In order that plot windows are displayed, you need to add PyPlot to your current environment via Pkg.add("PyPlot"). Often this automatic installation fails and it is recommended to follow instead the instructions Installing PyPlot in a robust way.

Release Notes

Version 0.5.2

Version 0.5.1

Version 0.5.0

Version 0.4.0

Version 0.3.1

Version 0.3.0

Version 0.2.6

Version 0.2.5

Version 0.2.4

Version 0.2.3

Version 0.2.2

Version 0.2.1

Version 0.2.0