mathematics

Cameo Simulation Toolkit: You can use Mathematica as an external maths engine to share maths between an OpaqueBehavior and a ConstraintBlock using custom auto-loaded Mathematica functions (keeps a project nice and DRY and respects Single Source of Truth)

Modelica references and links

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Just some links to handy Modelica references and educational resources.

HOWTO access custom (user-defined) Mathematica functions using Mathematica v13.2 as an external maths engine for SysML Parametrics (ConstraintBlocks) in Magic Model Analyst (Cameo Simulation Toolkit) versions 2021x, 2021xR1, 2022xR1

Mathematica + Magic Model Analyst (Cameo Simulation Toolkit) for SysML Parametrics: GOTCHA: You must use a regular '=' on the SysML side, not the Mathematica '==' (or it will be intepreted as a constraint condition to test, not an equation to solve).

HOWTO use Mathematica v12.3.2 as an external maths engine for SysML Parametrics (ConstraintBlocks) in Magic Model Analyst (Cameo Simulation Toolkit) versions 2021x, 2021xR1, 2022xR1

Webel: The single biggest disease in the world of IT is the idea that somehow mathematics is bad, or not useful, or not efficient, and that getting people who don't like maths to make stuff up (badly) in coding languages (rather than using maths) is ok.

TIP/GOTCHA: MagicDraw SysML/Cameo: In Parametric Diagrams create BindingConnectors involving part properties by selecting the constraint parameter symbol first and use the smart manipulator (otherwise you might accidentally create a regular Connector)

Q: What types of simulation, execution, and calculation are available for SysML with MagicDraw/Cameo?

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There are a number of ways of simulating and executing various aspects of Systems Modeling Language v1 (SysML^®), and they are not just novelties! They also really help your models become more robust, logical, and organised.

There is "internal" tool simulation of Activities and StateMachines based on fUML (or variations of it).

External simulation: Languages and tools: SysML vs SysPhS vs Modelica vs Simulink

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Tutorial

MINI TRAIL: Some recommended tools for getting started with Model-Based Systems Engineering with SysML and simulation with Modelica and/or Simulink

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OpenModelica zone

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If you use the Modelica Language for simulation it's basically a rite of passage to at least try out OpenModelica, although your mileage on various operating systems and versions thereof can vary wildly (you can always ask for the money back that you didn't pay).

As of 2021-01-11 OpenModelica no longer has DMG install bundles for Mac, and currently does NOT install on Mac Big Sur using MacPorts!

The parametric diagram is a new SysML diagram type that describes the constraints among the properties associated with blocks. This diagram is used to integrate behavior and structure models with engineering analysis models such as performance, ...

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OMG Systems Modeling Language (SysML) 1.6

A Complex value type represents the mathematical concept of a complex number. A complex number consists of a real part defined by a real number, and an imaginary part defined by a real number multiplied by the square root of -1 ...

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OMG Systems Modeling Language (SysML) 1.6

A PrimitiveType defines a predefined DataType, without any substructure. A PrimitiveType may have algebra and operations defined outside of UML, for example, mathematically.

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Unified Modeling Language 2.5.1

MagicDraw/Cameo support for the SysML Parametric Diagram and ConstraintBlocks for equations and mathematics is excellent, and it integrates with powerful maths engines such as Mathematica. It CAN be used on industrial strength real-world projects.

The SysML Parametric Diagram and the ContraintBlock technology for equations and mathematics is clever, powerful, useful, and integrates well with the other model-based engineering aspects of SysML.

10:01: [LINKS TO EXAMPLES] ConstraintBlocks: equations, parametrics, and mathematics in SysML

TRAIL: Webel's ultimate guide to Systems Modeling Language (v1) with MagicDraw/Cameo

MagicDraw/Cameo can parse the 'text' field of some mathematical Requirements and populate the constraint (and also then the constraint parameters) of a ConstraintBlock that refines a Requirement (your mileage varies).

Figure 8-10: Model library for primitive value types

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Tutorial

TRAIL: The SysML-1.6 Hybrid SUV sample and specification diagrams in MagicDraw/Cameo (with annotations) [UNDERGOING UPDATE to SysML1.7]

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Section: SysML-1.6 specification diagrams: 08 Blocks

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UML Profile Diagram

The constraints and parameters in Figure D.33 are detailed in Figure D.34 in Block Definition Diagram format. Note the use of valueTypes [ValueTypes] originally defined in Figure D.2.

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OMG Systems Modeling Language (SysML) 1.6

Figure D.34 - Defining Straight-Line Vehicle Dynamics Mathematical Constraints (Definition of Dynamics)

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Tutorial

TRAIL: The SysML-1.6 Hybrid SUV sample and specification diagrams in MagicDraw/Cameo (with annotations) [UNDERGOING UPDATE to SysML1.7]

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Section: SysML-1.6: HSUV sample

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SysML Block Definition Diagram (BDD)

Figure D.26 - Defining Analyses for Hybrid SUV Engineering Development (Block Definition Diagram)

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Tutorial

TRAIL: The SysML-1.6 Hybrid SUV sample and specification diagrams in MagicDraw/Cameo (with annotations) [UNDERGOING UPDATE to SysML1.7]

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Section: SysML-1.6: HSUV sample

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SysML Block Definition Diagram (BDD)

Webel: SysML: You don't need to call every ConstraintBlock a 'SomethingEquation'

Figure D.26 defines the various model elements that will be used to conduct analysis in this example. It depicts each of the constraint blocks/equations that will be used for the analysis, and key relationships between them.

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OMG Systems Modeling Language (SysML) 1.6

The context for the usages of constraint blocks shall also be specified in a parametric diagram to maintain the proper namespace for the nested properties.

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OMG Systems Modeling Language (SysML) 1.6

This allows a value property (such as an engine displacement) that may be deeply nested within a containing hierarchy (such as vehicle, power system, engine) to be referenced at the outer containing level (such as vehicle-level equations).

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OMG Systems Modeling Language (SysML) 1.6

A pathname dot notation can be used to refer to nested properties within a block hierarchy.

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OMG Systems Modeling Language (SysML) 1.6

The constrained properties, such as mass or response time, typically have simple value types that may also carry units, quantity kinds, or probability distributions.

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OMG Systems Modeling Language (SysML) 1.6

The usage of a constraint binds the parameters of the constraint, such as F, m, and a, to specific properties of a block, such as a mass, that provide values for the parameters.

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OMG Systems Modeling Language (SysML) 1.6

Parametric diagrams include usages of constraint blocks to constrain the properties of another block.

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OMG Systems Modeling Language (SysML) 1.6

The constraints can be nested to enable a constraint to be defined in terms of more basic constraints such as primitive mathematical operators.

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OMG Systems Modeling Language (SysML) 1.6

Reusable constraint definitions may be specified on block definition diagrams and packaged into general-purpose or domain-specific model libraries. Such constraints can be arbitrarily complex mathematical or logical expressions.

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OMG Systems Modeling Language (SysML) 1.6

Constraint blocks define generic forms of constraints that can be used in multiple contexts. For example, a definition for Newton’s Laws may be used to specify these constraints in many different contexts.

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OMG Systems Modeling Language (SysML) 1.6

A constraint block includes the constraint, such as {F=m*a}, and the parameters of the constraint such as F, m, and a.

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OMG Systems Modeling Language (SysML) 1.6

Such constraints can also be used to identify critical performance parameters and their relationships to other parameters, which can be tracked throughout the system life cycle.

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OMG Systems Modeling Language (SysML) 1.6

Constraint blocks can be used to specify a network of constraints that represent mathematical expressions such as {F=m*a} and {a=dv/dt}, which constrain the physical properties of a system.

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OMG Systems Modeling Language (SysML) 1.6

HERA particle collider beam dynamics: Maple symbolic worksheet example.

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This Maple worksheet download was exported to PDF via LaTeX from a Maple V worksheet. It shows detailed symbolic calculations and numerical simulations for the electron beam of the HERA (electron-proton synchrotron particle collider)].

Gallery: Maple examples: symbolic algebra, data visualisation, and animation

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Example of numerical integration and visualisation of a differential equation in the Maple symbolic algebra system

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Maple 3d plot animation example

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Maple example: symbolic algebra equation and numerical solution

Images in this gallery section

Click on any image to view it larger in a viewer, click again to move through each image in the gallery section. Click on the title link of an image to view the full image page.

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Example of numerical integration and visualisation of a differential equation in the Maple symbolic algebra system

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Maple 3d plot animation example

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Maple example: symbolic algebra equation and numerical solution

Maple zone

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Mathematica and Wolfram Language zone

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Please email or phone Webel IT Australia on +61 405 029 008 to enquire about our Mathematica services!

Webel IT Australia offers professional consultancy services for applications of the incredibly powerful Wolfram Mathematica to mathematical modelling, data analysis and visualisation, 3D modelling and animation, systems modelling, and physics modelling.