Adapt README and docs

Author: MartinOtter

README.md

@@ -1,29 +1,103 @@
-# ModiaLang.jl
+# Modia.jl
 
-[![The MIT License](https://img.shields.io/badge/license-MIT-brightgreen.svg?style=flat-square)](https://github.com/ModiaSim/ModiaLang.jl/blob/master/LICENSE.md)
+[![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://modiasim.github.io/Modia.jl/stable)
+[![The MIT License](https://img.shields.io/badge/license-MIT-brightgreen.svg?style=flat-square)](https://github.com/ModiaSim/Modia.jl/blob/master/LICENSE)
 
-ModiaLang is part of [ModiaSim](https://modiasim.github.io/docs/).
+The [Modia Tutorial](https://modiasim.github.io/Modia.jl/stable/tutorial/GettingStarted.html) provides an introduction to Modia.
+The [Modia3D Tutorial](https://modiasim.github.io/Modia3D.jl/stable/tutorial/GettingStarted.html) provides an introduction to use 3D components in Modia.
+Modia is part of [ModiaSim](https://modiasim.github.io/docs/).
 
-ModiaLang is usually used via [Modia](https://github.com/ModiaSim/Modia.jl).
-
-ModiaLang provides the core equation-based language of Modia, transformation of a model to ODE form dx/dt = f(x,t) and a thin interface to [DifferentialEquations](https://github.com/SciML/DifferentialEquations.jl).
+[Modia](https://github.com/ModiaSim/Modia.jl) is an environment in form of a Julia package to model and simulate physical systems (electrical, mechanical, thermo-dynamical, etc.) described by differential and algebraic equations. A user defines a model on a high level with model components (like a mechanical body, an electrical resistance, or a pipe) that are physically connected together. A model component is constructed by **`expression = expression` equations** or by Julia structs/functions, such as the pre-defined Modia 3D-mechanical components. The defined model is symbolically processed (for example, equations might be analytically differentiated) with algorithms from package [ModiaBase.jl](https://github.com/ModiaSim/ModiaBase.jl). From the transformed model a Julia function is generated that is used to simulate the model with integrators from [DifferentialEquations.jl](https://github.com/SciML/DifferentialEquations.jl).
+The basic type of the floating point variables is usually `Float64`, but can be set to any
+type `FloatType<:AbstractFloat` via `@instantiateModel(..., FloatType = xxx)`, for example
+it can be set to `Float32, DoubleFloat, Measurement{Float64}, StaticParticles{Float64,100}`.
 
 ## Installation
- 
-Typically, a user installs [Modia](https://github.com/ModiaSim/Modia.jl) and does not need
-to install ModiaLang separately. 
 
-If needed, ModiaLang is installed with (Julia >= 1.5 is required):
+The package is registered and is installed with (Julia >= 1.7 is required):
+
+```julia
+julia> ]add Modia
+```
+
+Furthermore, one or more of the following packages should be installed in order
+to be able to generate plots:
+
+```julia
+julia> ]add ModiaPlot_PyPlot        # if plotting with PyPlot desired
+        add ModiaPlot_GLMakie       # if plotting with GLMakie desired
+        add ModiaPlot_WGLMakie      # if plotting with WGLMakie desired
+        add ModiaPlot_CairoMakie    # if plotting with CairoMakie desired
+```
+
+Note, Modia exports all exported symbols of 
+
+- [DifferentialEquations](https://github.com/SciML/DifferentialEquations.jl) and of 
+- [Unitful](https://github.com/PainterQubits/Unitful.jl)
+
+
+## Examples
+
+The following equations describe a damped pendulum:
+
+![Pendulum-Equations](docs/resources/images/PendulumEquations.png)
+
+
+where *phi* is the rotation angle, *omega* the angular velocity, *m* the mass, *L* the rod length, *d* a damping constant, *g* the gravity constant and *r* the vector from the origin of the world system to the tip of the pendulum. These equations can be defined, simulated and plotted with
+(note, you can define models also without units, or remove units before the model is processed):
 
 ```julia
-julia> ]add ModiaLang
+using Modia
+@usingModiaPlot  # Use plot package defined with 
+                 # ENV["MODIA_PLOT"] or Modia.usePlotPackage(..)
+
+Pendulum = Model(
+   L = 0.8u"m",
+   m = 1.0u"kg",
+   d = 0.5u"N*m*s/rad",
+   g = 9.81u"m/s^2",
+   phi = Var(init = 1.57*u"rad"),
+   w   = Var(init = 0u"rad/s"),
+   equations = :[
+          w = der(phi)
+        0.0 = m*L^2*der(w) + d*w + m*g*L*sin(phi)
+          r = [L*cos(phi), -L*sin(phi)]
+   ]
+)
+
+pendulum1 = @instantiateModel(Pendulum)
+simulate!(pendulum1, Tsit5(), stopTime = 10.0u"s", log=true)
+plot(pendulum1, [("phi", "w"); "r"], figure = 1)
 ```
 
+The result is the following plot:
+
+![Pendulum-Figure](docs/resources/images/PendulumFigures.png)
+
+Simulation and plotting of the pendulum with normally distributed uncertainty added to some parameters is performed in the following way:
+
+```julia
+using Measurements
+
+PendulumWithUncertainties = Pendulum | Map(L = (0.8 ± 0.2)u"m",
+                                           m = (1.0 ± 0.2)u"kg",
+                                           d = (0.5 ± 0.2)u"N*m*s/rad")
+
+pendulum2 =  @instantiateModel(PendulumWithUncertainties,
+                               FloatType = Measurement{Float64})
+
+simulate!(pendulum2, Tsit5(), stopTime = 10.0u"s")
+plot(pendulum2, [("phi", "w"); "r"], figure = 2)
+```
+
+resulting in the following plot where mean values are shown with thick lines
+and standard deviations as area around the mean values.
+
+![PendulumWithUncertainty](docs/resources/images/PendulumWithUncertainties.png)
+
 ## Main Developers
 
 - [Hilding Elmqvist](mailto:[email protected]), [Mogram](http://www.mogram.net/).
-
 - [Martin Otter](https://rmc.dlr.de/sr/en/staff/martin.otter/),
   [DLR - Institute of System Dynamics and Control](https://www.dlr.de/sr/en).
 
-License: MIT (expat)

docs/src/Functions.md

@@ -1,7 +1,7 @@
 # Functions
 
 ```@meta
-CurrentModule = ModiaLang
+CurrentModule = Modia
 ```
 
 
@@ -35,7 +35,7 @@ The following functions are provided (for details see
 [Functions of ModiaResult](https://modiasim.github.io/ModiaResult.jl/stable/Functions.html#Functions-of-ModiaResult)):
 
 ```@meta
-CurrentModule = ModiaLang
+CurrentModule = Modia
 ```
 
 | Functions                        | Description                                       |